From 0f970e73fe55277643a5ffea6437eed6df0eef90 Mon Sep 17 00:00:00 2001
From: Daniel <dcolinmorgan@gmail.com>
Date: Mon, 25 Mar 2024 14:20:49 +0800
Subject: [PATCH 1/5] cleaned up notebooks added to gfql demo folder, readme
 update

---
 README.md                              |    4 +-
 demos/gfql/gfql_cpv_gpu_enchmark.ipynb | 2976 ++++++++++++++++++++++++
 demos/gfql/simple_gfql_notebook.ipynb  |  264 +++
 3 files changed, 3242 insertions(+), 2 deletions(-)
 create mode 100644 demos/gfql/gfql_cpv_gpu_enchmark.ipynb
 create mode 100644 demos/gfql/simple_gfql_notebook.ipynb

diff --git a/README.md b/README.md
index b4dcae3167..3a8fbb2166 100644
--- a/README.md
+++ b/README.md
@@ -147,7 +147,7 @@ It is easy to turn arbitrary data into insightful graphs. PyGraphistry comes wit
     g2.plot()
     ```
 
-* GFQL: Cypher-style graph pattern mining queries on dataframes with optional GPU acceleration ([ipynb demo](demos/more_examples/graphistry_features/hop_and_chain_graph_pattern_mining.ipynb), [benchmark](demos/gfql/benchmark_hops_cpu_gpu.ipynb))
+* GFQL: Cypher-style graph pattern mining queries on dataframes with optional GPU acceleration ([ipynb demo](demos/more_examples/graphistry_features/hop_and_chain_graph_pattern_mining.ipynb), [chain and hop demo](demos/gfql/simple_gfql_notebook.ipynb), [benchmark](demos/gfql/gfql_cpv_gpu_enchmark.ipynb)
 
   Run Cypher-style graph queries natively on dataframes without going to a database or Java with GFQL:
 
@@ -1248,7 +1248,7 @@ assert 'pagerank' in g2._nodes.columns
 
 PyGraphistry supports GFQL, its PyData-native variant of the popular Cypher graph query language, meaning you can do graph pattern matching directly from Pandas dataframes without installing a database or Java
 
-See also [graph pattern matching tutorial](demos/more_examples/graphistry_features/hop_and_chain_graph_pattern_mining.ipynb) and the CPU/GPU [benchmark](demos/gfql/benchmark_hops_cpu_gpu.ipynb)
+See also [graph pattern matching tutorial](demos/more_examples/graphistry_features/hop_and_chain_graph_pattern_mining.ipynb), [starting with chain and hop](demos/gfql/simple_gfql_notebook.ipynb) and the CPU/GPU [benchmark](demos/gfql/gfql_cpv_gpu_enchmark.ipynb)
 
 Traverse within a graph, or expand one graph against another
 
diff --git a/demos/gfql/gfql_cpv_gpu_enchmark.ipynb b/demos/gfql/gfql_cpv_gpu_enchmark.ipynb
new file mode 100644
index 0000000000..9860cc105e
--- /dev/null
+++ b/demos/gfql/gfql_cpv_gpu_enchmark.ipynb
@@ -0,0 +1,2976 @@
+{
+  "cells": [
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "view-in-github",
+        "colab_type": "text"
+      },
+      "source": [
+        "<a href=\"https://colab.research.google.com/github/dcolinmorgan/grph/blob/main/clean_gfql_cpu_gpu_benchmark.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "GZxoiU8sQDk_"
+      },
+      "source": [
+        "# GFQL CPU, GPU Benchmark\n",
+        "\n",
+        "This notebook examines GFQL property graph query performance on 1-8 hop queries using CPU + GPU modes on various real-world 100K - 100M edge graphs. The data comes from a variety of popular social networks. The single-threaded CPU mode benefits from GFQL's novel dataframe engine, and the GPU mode further adds single-GPU acceleration. Both the `chain()` and `hop()` methods are examined.\n",
+        "\n",
+        "The benchmark does not examine bigger-than-memory and distributed scenarios. The provided results here are from running on a free Google Colab T4 runtime, with a 2.2GHz Intel CPU (12 GB CPU RAM) and T4 Nvidia GPU (16 GB GPU RAM).\n",
+        "\n",
+        "## Data\n",
+        "From [SNAP](https://snap.stanford.edu/data/)\n",
+        "\n",
+        "| Network | Nodes     | Edges        |\n",
+        "|-------------|-----------|--------------|\n",
+        "| [**Facebook**](#fb)| 4,039     | 88,234       |\n",
+        "| [**Twitter**](#tw) | 81,306    | 2,420,766    |\n",
+        "| [**GPlus**](#gpl)   | 107,614   | 30,494,866   |\n",
+        "| [**Orkut**](#ork)   | 3,072,441 | 117,185,082  |\n",
+        "\n",
+        "## Results\n",
+        "\n",
+        "Definitions:\n",
+        "\n",
+        "* GTEPS: Giga (billion) edges traversed per second\n",
+        "\n",
+        "* T edges / \\$: Estimated trillion edges traversed for 1\\$ USD based on observed GTEPS and a 3yr AWS reservation (as of 12/2023)\n",
+        "\n",
+        "Tasks:\n",
+        "\n",
+        "1. `chain()` - includes complex pre/post processing\n",
+        "\n",
+        "  **Task**: `g.chain([n({'id': some_id}), e_forward(hops=some_n)])`\n",
+        "\n",
+        "\n",
+        "| **Dataset** | Max GPU Speedup      | CPU GTEPS   | GPU GTEPS   | T CPU edges / \\$ (t3.l) | T GPU edges / \\$ (g4dn.xl) |\n",
+        "|-------------|--------------|-------------|-------------|----------------------------|--------------------------------|\n",
+        "| [**Facebook**](#fb)| 1.1X  | 0.66 | 0.61 | 65.7                | 10.4                    |\n",
+        "| [**Twitter**](#tw) | 17.4X   | 0.17 | 2.81 | 16.7                | 48.1                    |\n",
+        "| [**GPlus**](#gpl)   | 43.8X  | 0.09 | 2.87 | 8.5                | 49.2                    |\n",
+        "| [**Orkut**](#ork)   | N/A            | N/A         | 12.15 | N/A                        | 208.3                    |\n",
+        "| **AVG** | 20.7X | 0.30 | 4.61 | 30.3 | 79.0\n",
+        "| **MAX** | 43.8X | 0.66 | 12.15 | 65.7 | 208.3\n",
+        "\n",
+        "\n",
+        "2. `hop()` - core property search primitive similar to BFS\n",
+        "\n",
+        "  **Task**: `g.hop(nodes=[some_id], direction='forward', hops=some_n)`\n",
+        "\n",
+        "\n",
+        "| **Dataset** | Max GPU Speedup | CPU GTEPS | GPU GTEPS | T CPU edges / \\$ (t3.l) | T GPU edges / \\$ (g4dn.xl) |\n",
+        "|-------------|-------------|-----------|-----------|--------------------|--------------------------------|\n",
+        "| [**Facebook**](#fb)| 3X          | 0.47      | 1.47     | 47.0        | 25.2                    |\n",
+        "| [**Twitter**](#tw) | 42X         | 0.50      | 10.51      | 50.2        | 180.2                    |\n",
+        "| [**GPlus**](#gpl)   | 21X         | 0.26      | 4.11       | 26.2        | 70.4                    |\n",
+        "| [**Orkut**](#ork)   | N/A         | N/A       | 41.50     | N/A                | 711.4                    |\n",
+        "| **AVG** | 22X | 0.41 | 14.4 | 41.1 | 246.8\n",
+        "| **MAX** | 42X | 0.50 | 41.50 | 50.2 | 711.4\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "SAj8lhREEOwS"
+      },
+      "source": [
+        "## Optional: GPU setup - Google Colab"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "4hrEEAAm7DTO"
+      },
+      "source": []
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "W2MF6ZsjDv3B",
+        "outputId": "d09118ee-55d5-49cf-b950-d1e232aa4eb2"
+      },
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "Mon Feb 19 04:14:57 2024       \n",
+            "+---------------------------------------------------------------------------------------+\n",
+            "| NVIDIA-SMI 535.104.05             Driver Version: 535.104.05   CUDA Version: 12.2     |\n",
+            "|-----------------------------------------+----------------------+----------------------+\n",
+            "| GPU  Name                 Persistence-M | Bus-Id        Disp.A | Volatile Uncorr. ECC |\n",
+            "| Fan  Temp   Perf          Pwr:Usage/Cap |         Memory-Usage | GPU-Util  Compute M. |\n",
+            "|                                         |                      |               MIG M. |\n",
+            "|=========================================+======================+======================|\n",
+            "|   0  Tesla T4                       Off | 00000000:00:04.0 Off |                    0 |\n",
+            "| N/A   39C    P8               9W /  70W |      0MiB / 15360MiB |      0%      Default |\n",
+            "|                                         |                      |                  N/A |\n",
+            "+-----------------------------------------+----------------------+----------------------+\n",
+            "                                                                                         \n",
+            "+---------------------------------------------------------------------------------------+\n",
+            "| Processes:                                                                            |\n",
+            "|  GPU   GI   CI        PID   Type   Process name                            GPU Memory |\n",
+            "|        ID   ID                                                             Usage      |\n",
+            "|=======================================================================================|\n",
+            "|  No running processes found                                                           |\n",
+            "+---------------------------------------------------------------------------------------+\n"
+          ]
+        }
+      ],
+      "source": [
+        "# Report GPU used when GPU benchmarking\n",
+        "! nvidia-smi"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "id": "Aikh0x4ID_wK"
+      },
+      "outputs": [],
+      "source": [
+        "# if in google colab\n",
+        "# !git clone https://github.com/rapidsai/rapidsai-csp-utils.git\n",
+        "# !python rapidsai-csp-utils/colab/pip-install.py\n",
+        "!pip install --extra-index-url=https://pypi.nvidia.com cuml-cu12 cudf-cu12 #==23.12.00 #cugraph-cu11 pylibraft_cu11 raft_dask_cu11 dask_cudf_cu11 pylibcugraph_cu11 pylibraft_cu11\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 35
+        },
+        "id": "Lwekdei1dH3N",
+        "outputId": "a506b4fb-0dba-4e90-884e-df16cb19eebd"
+      },
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "'24.02.01'"
+            ],
+            "application/vnd.google.colaboratory.intrinsic+json": {
+              "type": "string"
+            }
+          },
+          "metadata": {},
+          "execution_count": 2
+        }
+      ],
+      "source": [
+        "import cudf\n",
+        "cudf.__version__"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "QQpsrtwBT7sa"
+      },
+      "source": [
+        "# 1. Install & configure"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "cYjRbgkU9Sx8",
+        "outputId": "7d592f98-36af-4657-b8eb-80eeabd98e2f"
+      },
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m3.3/3.3 MB\u001b[0m \u001b[31m14.0 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
+            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m244.4/244.4 kB\u001b[0m \u001b[31m2.2 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
+            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m332.3/332.3 kB\u001b[0m \u001b[31m8.5 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
+            "\u001b[?25h"
+          ]
+        }
+      ],
+      "source": [
+        "#! pip install graphistry[igraph]\n",
+        "\n",
+        "!pip install -q igraph\n",
+        "!pip install -q graphistry\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "Ff6Tt9DhkePl"
+      },
+      "source": [
+        "## Imports"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 35
+        },
+        "id": "S5_y0CbLkjft",
+        "outputId": "909ff8a7-650e-4e65-aaf9-40f650d50145"
+      },
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "'0.33.0'"
+            ],
+            "application/vnd.google.colaboratory.intrinsic+json": {
+              "type": "string"
+            }
+          },
+          "metadata": {},
+          "execution_count": 4
+        }
+      ],
+      "source": [
+        "import pandas as pd\n",
+        "\n",
+        "import graphistry, time\n",
+        "\n",
+        "from graphistry import (\n",
+        "\n",
+        "    # graph operators\n",
+        "    n, e_undirected, e_forward, e_reverse,\n",
+        "\n",
+        "    # attribute predicates\n",
+        "    is_in, ge, startswith, contains, match as match_re\n",
+        ")\n",
+        "graphistry.__version__"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "id": "I7Fg75jsG4co"
+      },
+      "outputs": [],
+      "source": [
+        "import cudf"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "id": "uLZKph2-a5M4"
+      },
+      "outputs": [],
+      "source": [
+        "#work around google colab shell encoding bugs\n",
+        "\n",
+        "import locale\n",
+        "locale.getpreferredencoding = lambda: \"UTF-8\""
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "eU9SyauNUHtR"
+      },
+      "source": [
+        "# 2. Perf benchmarks"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "NA0Ym11fkB8j"
+      },
+      "source": [
+        "<a name=\"fb\"></a>\n",
+        "### Facebook: 88K edges"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 224
+        },
+        "id": "vXuQogHekClJ",
+        "outputId": "de95808f-d1c9-4864-e8d9-b197f3d38413"
+      },
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "(88234, 2)\n"
+          ]
+        },
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "   s  d\n",
+              "0  0  1\n",
+              "1  0  2\n",
+              "2  0  3\n",
+              "3  0  4\n",
+              "4  0  5"
+            ],
+            "text/html": [
+              "\n",
+              "  <div id=\"df-8d88e76b-5f6b-4c01-9976-d9cccf151e38\" class=\"colab-df-container\">\n",
+              "    <div>\n",
+              "<style scoped>\n",
+              "    .dataframe tbody tr th:only-of-type {\n",
+              "        vertical-align: middle;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe tbody tr th {\n",
+              "        vertical-align: top;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe thead th {\n",
+              "        text-align: right;\n",
+              "    }\n",
+              "</style>\n",
+              "<table border=\"1\" class=\"dataframe\">\n",
+              "  <thead>\n",
+              "    <tr style=\"text-align: right;\">\n",
+              "      <th></th>\n",
+              "      <th>s</th>\n",
+              "      <th>d</th>\n",
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+              "      <td>0</td>\n",
+              "      <td>5</td>\n",
+              "    </tr>\n",
+              "  </tbody>\n",
+              "</table>\n",
+              "</div>\n",
+              "    <div class=\"colab-df-buttons\">\n",
+              "\n",
+              "  <div class=\"colab-df-container\">\n",
+              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-8d88e76b-5f6b-4c01-9976-d9cccf151e38')\"\n",
+              "            title=\"Convert this dataframe to an interactive table.\"\n",
+              "            style=\"display:none;\">\n",
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+              "  </svg>\n",
+              "    </button>\n",
+              "\n",
+              "  <style>\n",
+              "    .colab-df-container {\n",
+              "      display:flex;\n",
+              "      gap: 12px;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-convert {\n",
+              "      background-color: #E8F0FE;\n",
+              "      border: none;\n",
+              "      border-radius: 50%;\n",
+              "      cursor: pointer;\n",
+              "      display: none;\n",
+              "      fill: #1967D2;\n",
+              "      height: 32px;\n",
+              "      padding: 0 0 0 0;\n",
+              "      width: 32px;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-convert:hover {\n",
+              "      background-color: #E2EBFA;\n",
+              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
+              "      fill: #174EA6;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-buttons div {\n",
+              "      margin-bottom: 4px;\n",
+              "    }\n",
+              "\n",
+              "    [theme=dark] .colab-df-convert {\n",
+              "      background-color: #3B4455;\n",
+              "      fill: #D2E3FC;\n",
+              "    }\n",
+              "\n",
+              "    [theme=dark] .colab-df-convert:hover {\n",
+              "      background-color: #434B5C;\n",
+              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
+              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
+              "      fill: #FFFFFF;\n",
+              "    }\n",
+              "  </style>\n",
+              "\n",
+              "    <script>\n",
+              "      const buttonEl =\n",
+              "        document.querySelector('#df-8d88e76b-5f6b-4c01-9976-d9cccf151e38 button.colab-df-convert');\n",
+              "      buttonEl.style.display =\n",
+              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
+              "\n",
+              "      async function convertToInteractive(key) {\n",
+              "        const element = document.querySelector('#df-8d88e76b-5f6b-4c01-9976-d9cccf151e38');\n",
+              "        const dataTable =\n",
+              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
+              "                                                    [key], {});\n",
+              "        if (!dataTable) return;\n",
+              "\n",
+              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
+              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
+              "          + ' to learn more about interactive tables.';\n",
+              "        element.innerHTML = '';\n",
+              "        dataTable['output_type'] = 'display_data';\n",
+              "        await google.colab.output.renderOutput(dataTable, element);\n",
+              "        const docLink = document.createElement('div');\n",
+              "        docLink.innerHTML = docLinkHtml;\n",
+              "        element.appendChild(docLink);\n",
+              "      }\n",
+              "    </script>\n",
+              "  </div>\n",
+              "\n",
+              "\n",
+              "<div id=\"df-027a4397-12aa-439e-93da-49eac22ef242\">\n",
+              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-027a4397-12aa-439e-93da-49eac22ef242')\"\n",
+              "            title=\"Suggest charts\"\n",
+              "            style=\"display:none;\">\n",
+              "\n",
+              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
+              "     width=\"24px\">\n",
+              "    <g>\n",
+              "        <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
+              "    </g>\n",
+              "</svg>\n",
+              "  </button>\n",
+              "\n",
+              "<style>\n",
+              "  .colab-df-quickchart {\n",
+              "      --bg-color: #E8F0FE;\n",
+              "      --fill-color: #1967D2;\n",
+              "      --hover-bg-color: #E2EBFA;\n",
+              "      --hover-fill-color: #174EA6;\n",
+              "      --disabled-fill-color: #AAA;\n",
+              "      --disabled-bg-color: #DDD;\n",
+              "  }\n",
+              "\n",
+              "  [theme=dark] .colab-df-quickchart {\n",
+              "      --bg-color: #3B4455;\n",
+              "      --fill-color: #D2E3FC;\n",
+              "      --hover-bg-color: #434B5C;\n",
+              "      --hover-fill-color: #FFFFFF;\n",
+              "      --disabled-bg-color: #3B4455;\n",
+              "      --disabled-fill-color: #666;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart {\n",
+              "    background-color: var(--bg-color);\n",
+              "    border: none;\n",
+              "    border-radius: 50%;\n",
+              "    cursor: pointer;\n",
+              "    display: none;\n",
+              "    fill: var(--fill-color);\n",
+              "    height: 32px;\n",
+              "    padding: 0;\n",
+              "    width: 32px;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart:hover {\n",
+              "    background-color: var(--hover-bg-color);\n",
+              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
+              "    fill: var(--button-hover-fill-color);\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart-complete:disabled,\n",
+              "  .colab-df-quickchart-complete:disabled:hover {\n",
+              "    background-color: var(--disabled-bg-color);\n",
+              "    fill: var(--disabled-fill-color);\n",
+              "    box-shadow: none;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-spinner {\n",
+              "    border: 2px solid var(--fill-color);\n",
+              "    border-color: transparent;\n",
+              "    border-bottom-color: var(--fill-color);\n",
+              "    animation:\n",
+              "      spin 1s steps(1) infinite;\n",
+              "  }\n",
+              "\n",
+              "  @keyframes spin {\n",
+              "    0% {\n",
+              "      border-color: transparent;\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "      border-left-color: var(--fill-color);\n",
+              "    }\n",
+              "    20% {\n",
+              "      border-color: transparent;\n",
+              "      border-left-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "    }\n",
+              "    30% {\n",
+              "      border-color: transparent;\n",
+              "      border-left-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "      border-right-color: var(--fill-color);\n",
+              "    }\n",
+              "    40% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "    }\n",
+              "    60% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "    }\n",
+              "    80% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "    }\n",
+              "    90% {\n",
+              "      border-color: transparent;\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "    }\n",
+              "  }\n",
+              "</style>\n",
+              "\n",
+              "  <script>\n",
+              "    async function quickchart(key) {\n",
+              "      const quickchartButtonEl =\n",
+              "        document.querySelector('#' + key + ' button');\n",
+              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
+              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
+              "      try {\n",
+              "        const charts = await google.colab.kernel.invokeFunction(\n",
+              "            'suggestCharts', [key], {});\n",
+              "      } catch (error) {\n",
+              "        console.error('Error during call to suggestCharts:', error);\n",
+              "      }\n",
+              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
+              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
+              "    }\n",
+              "    (() => {\n",
+              "      let quickchartButtonEl =\n",
+              "        document.querySelector('#df-027a4397-12aa-439e-93da-49eac22ef242 button');\n",
+              "      quickchartButtonEl.style.display =\n",
+              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
+              "    })();\n",
+              "  </script>\n",
+              "</div>\n",
+              "    </div>\n",
+              "  </div>\n"
+            ],
+            "application/vnd.google.colaboratory.intrinsic+json": {
+              "type": "dataframe",
+              "variable_name": "df",
+              "summary": "{\n  \"name\": \"df\",\n  \"rows\": 88234,\n  \"fields\": [\n    {\n      \"column\": \"s\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 910,\n        \"min\": 0,\n        \"max\": 4031,\n        \"samples\": [\n          1624,\n          101,\n          377\n        ],\n        \"num_unique_values\": 3663,\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"d\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 893,\n        \"min\": 1,\n        \"max\": 4038,\n        \"samples\": [\n          2193,\n          150,\n          879\n        ],\n        \"num_unique_values\": 4037,\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
+            }
+          },
+          "metadata": {},
+          "execution_count": 7
+        }
+      ],
+      "source": [
+        "df = pd.read_csv('https://raw.githubusercontent.com/graphistry/pygraphistry/master/demos/data/facebook_combined.txt', sep=' ', names=['s', 'd'])\n",
+        "print(df.shape)\n",
+        "df.head(5)"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 224
+        },
+        "id": "jEma7hvvkzkN",
+        "outputId": "98501752-d3df-4f5d-95b8-ff085a17894a"
+      },
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "(4039, 1) (88234, 2)\n"
+          ]
+        },
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "   id\n",
+              "0   0\n",
+              "1   1\n",
+              "2   2\n",
+              "3   3\n",
+              "4   4"
+            ],
+            "text/html": [
+              "\n",
+              "  <div id=\"df-a6096f22-dea0-424e-b5b9-6a8685fb8eec\" class=\"colab-df-container\">\n",
+              "    <div>\n",
+              "<style scoped>\n",
+              "    .dataframe tbody tr th:only-of-type {\n",
+              "        vertical-align: middle;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe tbody tr th {\n",
+              "        vertical-align: top;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe thead th {\n",
+              "        text-align: right;\n",
+              "    }\n",
+              "</style>\n",
+              "<table border=\"1\" class=\"dataframe\">\n",
+              "  <thead>\n",
+              "    <tr style=\"text-align: right;\">\n",
+              "      <th></th>\n",
+              "      <th>id</th>\n",
+              "    </tr>\n",
+              "  </thead>\n",
+              "  <tbody>\n",
+              "    <tr>\n",
+              "      <th>0</th>\n",
+              "      <td>0</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>1</th>\n",
+              "      <td>1</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>2</th>\n",
+              "      <td>2</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>3</th>\n",
+              "      <td>3</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>4</th>\n",
+              "      <td>4</td>\n",
+              "    </tr>\n",
+              "  </tbody>\n",
+              "</table>\n",
+              "</div>\n",
+              "    <div class=\"colab-df-buttons\">\n",
+              "\n",
+              "  <div class=\"colab-df-container\">\n",
+              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-a6096f22-dea0-424e-b5b9-6a8685fb8eec')\"\n",
+              "            title=\"Convert this dataframe to an interactive table.\"\n",
+              "            style=\"display:none;\">\n",
+              "\n",
+              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
+              "    <path d=\"M120-120v-720h720v720H120Zm60-500h600v-160H180v160Zm220 220h160v-160H400v160Zm0 220h160v-160H400v160ZM180-400h160v-160H180v160Zm440 0h160v-160H620v160ZM180-180h160v-160H180v160Zm440 0h160v-160H620v160Z\"/>\n",
+              "  </svg>\n",
+              "    </button>\n",
+              "\n",
+              "  <style>\n",
+              "    .colab-df-container {\n",
+              "      display:flex;\n",
+              "      gap: 12px;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-convert {\n",
+              "      background-color: #E8F0FE;\n",
+              "      border: none;\n",
+              "      border-radius: 50%;\n",
+              "      cursor: pointer;\n",
+              "      display: none;\n",
+              "      fill: #1967D2;\n",
+              "      height: 32px;\n",
+              "      padding: 0 0 0 0;\n",
+              "      width: 32px;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-convert:hover {\n",
+              "      background-color: #E2EBFA;\n",
+              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
+              "      fill: #174EA6;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-buttons div {\n",
+              "      margin-bottom: 4px;\n",
+              "    }\n",
+              "\n",
+              "    [theme=dark] .colab-df-convert {\n",
+              "      background-color: #3B4455;\n",
+              "      fill: #D2E3FC;\n",
+              "    }\n",
+              "\n",
+              "    [theme=dark] .colab-df-convert:hover {\n",
+              "      background-color: #434B5C;\n",
+              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
+              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
+              "      fill: #FFFFFF;\n",
+              "    }\n",
+              "  </style>\n",
+              "\n",
+              "    <script>\n",
+              "      const buttonEl =\n",
+              "        document.querySelector('#df-a6096f22-dea0-424e-b5b9-6a8685fb8eec button.colab-df-convert');\n",
+              "      buttonEl.style.display =\n",
+              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
+              "\n",
+              "      async function convertToInteractive(key) {\n",
+              "        const element = document.querySelector('#df-a6096f22-dea0-424e-b5b9-6a8685fb8eec');\n",
+              "        const dataTable =\n",
+              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
+              "                                                    [key], {});\n",
+              "        if (!dataTable) return;\n",
+              "\n",
+              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
+              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
+              "          + ' to learn more about interactive tables.';\n",
+              "        element.innerHTML = '';\n",
+              "        dataTable['output_type'] = 'display_data';\n",
+              "        await google.colab.output.renderOutput(dataTable, element);\n",
+              "        const docLink = document.createElement('div');\n",
+              "        docLink.innerHTML = docLinkHtml;\n",
+              "        element.appendChild(docLink);\n",
+              "      }\n",
+              "    </script>\n",
+              "  </div>\n",
+              "\n",
+              "\n",
+              "<div id=\"df-857b100f-363e-41f4-8e2a-0628457e85bc\">\n",
+              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-857b100f-363e-41f4-8e2a-0628457e85bc')\"\n",
+              "            title=\"Suggest charts\"\n",
+              "            style=\"display:none;\">\n",
+              "\n",
+              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
+              "     width=\"24px\">\n",
+              "    <g>\n",
+              "        <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
+              "    </g>\n",
+              "</svg>\n",
+              "  </button>\n",
+              "\n",
+              "<style>\n",
+              "  .colab-df-quickchart {\n",
+              "      --bg-color: #E8F0FE;\n",
+              "      --fill-color: #1967D2;\n",
+              "      --hover-bg-color: #E2EBFA;\n",
+              "      --hover-fill-color: #174EA6;\n",
+              "      --disabled-fill-color: #AAA;\n",
+              "      --disabled-bg-color: #DDD;\n",
+              "  }\n",
+              "\n",
+              "  [theme=dark] .colab-df-quickchart {\n",
+              "      --bg-color: #3B4455;\n",
+              "      --fill-color: #D2E3FC;\n",
+              "      --hover-bg-color: #434B5C;\n",
+              "      --hover-fill-color: #FFFFFF;\n",
+              "      --disabled-bg-color: #3B4455;\n",
+              "      --disabled-fill-color: #666;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart {\n",
+              "    background-color: var(--bg-color);\n",
+              "    border: none;\n",
+              "    border-radius: 50%;\n",
+              "    cursor: pointer;\n",
+              "    display: none;\n",
+              "    fill: var(--fill-color);\n",
+              "    height: 32px;\n",
+              "    padding: 0;\n",
+              "    width: 32px;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart:hover {\n",
+              "    background-color: var(--hover-bg-color);\n",
+              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
+              "    fill: var(--button-hover-fill-color);\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart-complete:disabled,\n",
+              "  .colab-df-quickchart-complete:disabled:hover {\n",
+              "    background-color: var(--disabled-bg-color);\n",
+              "    fill: var(--disabled-fill-color);\n",
+              "    box-shadow: none;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-spinner {\n",
+              "    border: 2px solid var(--fill-color);\n",
+              "    border-color: transparent;\n",
+              "    border-bottom-color: var(--fill-color);\n",
+              "    animation:\n",
+              "      spin 1s steps(1) infinite;\n",
+              "  }\n",
+              "\n",
+              "  @keyframes spin {\n",
+              "    0% {\n",
+              "      border-color: transparent;\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "      border-left-color: var(--fill-color);\n",
+              "    }\n",
+              "    20% {\n",
+              "      border-color: transparent;\n",
+              "      border-left-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "    }\n",
+              "    30% {\n",
+              "      border-color: transparent;\n",
+              "      border-left-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "      border-right-color: var(--fill-color);\n",
+              "    }\n",
+              "    40% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "    }\n",
+              "    60% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "    }\n",
+              "    80% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "    }\n",
+              "    90% {\n",
+              "      border-color: transparent;\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "    }\n",
+              "  }\n",
+              "</style>\n",
+              "\n",
+              "  <script>\n",
+              "    async function quickchart(key) {\n",
+              "      const quickchartButtonEl =\n",
+              "        document.querySelector('#' + key + ' button');\n",
+              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
+              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
+              "      try {\n",
+              "        const charts = await google.colab.kernel.invokeFunction(\n",
+              "            'suggestCharts', [key], {});\n",
+              "      } catch (error) {\n",
+              "        console.error('Error during call to suggestCharts:', error);\n",
+              "      }\n",
+              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
+              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
+              "    }\n",
+              "    (() => {\n",
+              "      let quickchartButtonEl =\n",
+              "        document.querySelector('#df-857b100f-363e-41f4-8e2a-0628457e85bc button');\n",
+              "      quickchartButtonEl.style.display =\n",
+              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
+              "    })();\n",
+              "  </script>\n",
+              "</div>\n",
+              "    </div>\n",
+              "  </div>\n"
+            ],
+            "application/vnd.google.colaboratory.intrinsic+json": {
+              "type": "dataframe",
+              "summary": "{\n  \"name\": \"fg\",\n  \"rows\": 5,\n  \"fields\": [\n    {\n      \"column\": \"id\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 1,\n        \"min\": 0,\n        \"max\": 4,\n        \"samples\": [\n          1,\n          4,\n          2\n        ],\n        \"num_unique_values\": 5,\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
+            }
+          },
+          "metadata": {},
+          "execution_count": 8
+        }
+      ],
+      "source": [
+        "fg = graphistry.edges(df, 's', 'd').materialize_nodes()\n",
+        "print(fg._nodes.shape, fg._edges.shape)\n",
+        "fg._nodes.head(5)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "with 2 and 5 hop `chain` comparison we see a slight/negligable speedup enabled by setting g. to `cudf`"
+      ],
+      "metadata": {
+        "id": "2gVDho9cn2Et"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "for n_hop in [2,5]:\n",
+        "    start0 = time.time()\n",
+        "    for i in range(100):\n",
+        "        fg2 = fg.chain([n({'id': 0}), e_forward(hops=n_hop)])  # using n notation\n",
+        "    mid0 = time.time()\n",
+        "    for i in range(100):\n",
+        "        fg2 = fg.chain([e_forward(source_node_match={'id': 0}, hops=n_hop)])  # using source_node_match in e_forward\n",
+        "    end0 = time.time()\n",
+        "    T0 = mid0-start0\n",
+        "    T1 = end0-mid0\n",
+        "    fg_gdf = fg.nodes(lambda g: cudf.DataFrame(g._nodes)).edges(lambda g: cudf.DataFrame(g._edges))\n",
+        "    start1 = time.time()\n",
+        "    for i in range(100):\n",
+        "        fg2 = fg_gdf.chain([n({'id': 0}), e_forward(hops=n_hop)])\n",
+        "    mid1 = time.time()\n",
+        "    for i in range(100):\n",
+        "        fg2 = fg_gdf.chain([e_forward(source_node_match={'id': 0}, hops=n_hop)])\n",
+        "    end1 = time.time()\n",
+        "    # print(fg._nodes.shape, fg._edges.shape)\n",
+        "    # print(fg2._nodes.shape, fg2._edges.shape)\n",
+        "    del fg_gdf\n",
+        "    del fg2\n",
+        "    T2 = mid1-start1\n",
+        "    T3 = end1-mid1\n",
+        "    print('\\nhops:',n_hop,'\\nCPU n_notation time:',np.round(T0,4),'\\nGPU n_notation time:',np.round(T2,4),'\\nspeedup:', np.round(T0/T2,4),\n",
+        "          '\\nCPU source_node_match time:',np.round(T1,4),'\\nGPU source_node_match time:',np.round(T3,4),'\\nspeedup:', np.round(T1/T3,4), )"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "ZKzoqGcdxekr",
+        "outputId": "344b9823-6998-4f71-d3b5-7aff9fec7912"
+      },
+      "execution_count": null,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "hops: 2 \n",
+            "CPU n_notation time: 13.6357 \n",
+            "GPU n_notation time: 12.2177 \n",
+            "n_notation speedup: 1.1161 \n",
+            "CPU source_node_match time: 21.2028 \n",
+            "GPU source_node_match time: 14.3844 \n",
+            "source_node_match speedup: 1.474\n",
+            "hops: 5 \n",
+            "CPU n_notation time: 36.8941 \n",
+            "GPU n_notation time: 21.3562 \n",
+            "n_notation speedup: 1.7276 \n",
+            "CPU source_node_match time: 17.8739 \n",
+            "GPU source_node_match time: 14.8514 \n",
+            "source_node_match speedup: 1.2035\n"
+          ]
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "and with simple 2 and 5 hop `hop` comparison we see a 2x speedup enabled by setting g. to `cudf`"
+      ],
+      "metadata": {
+        "id": "5-7M9sPEAf5Z"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "for n_hop in [2,5]:\n",
+        "    start_nodes = pd.DataFrame({fg._node: [0]})\n",
+        "    start0 = time.time()\n",
+        "    for i in range(100):\n",
+        "        fg2 = fg.hop(\n",
+        "            nodes=start_nodes,\n",
+        "            direction='forward',\n",
+        "            hops=n_hop)\n",
+        "    end0 = time.time()\n",
+        "    T0 = end0-start0\n",
+        "    start_nodes = cudf.DataFrame({fg._node: [0]})\n",
+        "    fg_gdf = fg.nodes(cudf.from_pandas(fg._nodes)).edges(cudf.from_pandas(fg._edges))\n",
+        "    start1 = time.time()\n",
+        "    for i in range(100):\n",
+        "        fg2 = fg_gdf.hop(\n",
+        "            nodes=start_nodes,\n",
+        "            direction='forward',\n",
+        "            hops=n_hop)\n",
+        "    end1 = time.time()\n",
+        "    # print(fg._nodes.shape, fg._edges.shape)\n",
+        "    # print(fg2._nodes.shape, fg2._edges.shape)\n",
+        "    del fg_gdf\n",
+        "    del fg2\n",
+        "    T1 = end1-start1\n",
+        "    print('\\nCPU',n_hop,'hop time:',np.round(T0,4),'\\nGPU',n_hop,'hop time:',np.round(T1,4),'\\nspeedup:', np.round(T0/T1,4))"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "Tki_0-_j3XKG",
+        "outputId": "7edbb4e9-1f49-4b7a-fdb4-9df0867512cd"
+      },
+      "execution_count": null,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "\n",
+            "CPU 2 hop time: 5.7415 \n",
+            "GPU 2 hop time: 2.7301 2 \n",
+            "hop speedup: 2.103\n",
+            "\n",
+            "CPU 5 hop time: 14.3391 \n",
+            "GPU 5 hop time: 6.9998 5 \n",
+            "hop speedup: 2.0485\n"
+          ]
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "KrJKjXy2KLos"
+      },
+      "source": [
+        "<a name=\"tw\"></a>\n",
+        "## Twitter\n",
+        "\n",
+        "- edges: 2420766\n",
+        "- nodes: 81306"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "fO2qasGqpubr",
+        "outputId": "957c5ea8-0da9-4101-ecf8-7db8d5d13f49"
+      },
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "--2024-02-20 09:48:59--  https://snap.stanford.edu/data/twitter_combined.txt.gz\n",
+            "Resolving snap.stanford.edu (snap.stanford.edu)... 171.64.75.80\n",
+            "Connecting to snap.stanford.edu (snap.stanford.edu)|171.64.75.80|:443... connected.\n",
+            "HTTP request sent, awaiting response... 200 OK\n",
+            "Length: 10621918 (10M) [application/x-gzip]\n",
+            "Saving to: ‘twitter_combined.txt.gz’\n",
+            "\n",
+            "twitter_combined.tx 100%[===================>]  10.13M  9.10MB/s    in 1.1s    \n",
+            "\n",
+            "2024-02-20 09:49:00 (9.10 MB/s) - ‘twitter_combined.txt.gz’ saved [10621918/10621918]\n",
+            "\n"
+          ]
+        }
+      ],
+      "source": [
+        "! wget 'https://snap.stanford.edu/data/twitter_combined.txt.gz'\n",
+        "#! curl -L 'https://snap.stanford.edu/data/twitter_combined.txt.gz' -o twitter_combined.txt.gz"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "id": "fn7zeA3SGlEo"
+      },
+      "outputs": [],
+      "source": [
+        "! gunzip twitter_combined.txt.gz"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "68TAZkhLGz9g",
+        "outputId": "b861bc74-a142-4880-dc43-8068f7ef6b04"
+      },
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "214328887 34428380\n",
+            "17116707 28465635\n",
+            "380580781 18996905\n",
+            "221036078 153460275\n",
+            "107830991 17868918\n"
+          ]
+        }
+      ],
+      "source": [
+        "! head -n 5 twitter_combined.txt"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "QU2wNeGXG2GC",
+        "outputId": "dff04552-efc7-49a6-9f25-460f31a288be"
+      },
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "(2420766, 2)"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 31
+        }
+      ],
+      "source": [
+        "te_df = pd.read_csv('twitter_combined.txt', sep=' ', names=['s', 'd'])\n",
+        "te_df.shape"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "id": "EK5gQH2iG5UU"
+      },
+      "outputs": [],
+      "source": [
+        "import graphistry"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "ZtIW-eFGG_R4",
+        "outputId": "53bd4e96-f3c4-4d45-abfd-e8a454a8ac7e"
+      },
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "(81306, 1)"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 33
+        }
+      ],
+      "source": [
+        "g = graphistry.edges(te_df, 's', 'd').materialize_nodes()\n",
+        "g._nodes.shape"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "on the twitter data, simpler `chain` operations over several different hops -- **10-20x** *italicized text* speed increases"
+      ],
+      "metadata": {
+        "id": "yR9Qr8tGww3b"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "for n_hop in [1,2,8]:\n",
+        "    start_nodes = pd.DataFrame({fg._node: [0]})\n",
+        "    start0 = time.time()\n",
+        "    for i in range(10):\n",
+        "        g2 = g.chain([n({'id': 17116707}), e_forward(hops=n_hop)])\n",
+        "    end0 = time.time()\n",
+        "    T0 = end0-start0\n",
+        "    g_gdf = g.nodes(lambda g: cudf.DataFrame(g._nodes)).edges(lambda g: cudf.DataFrame(g._edges))\n",
+        "    start1 = time.time()\n",
+        "    for i in range(10):\n",
+        "        out = g_gdf.chain([n({'id': 17116707}), e_forward(hops=n_hop)])._nodes\n",
+        "    end1 = time.time()\n",
+        "    # print(fg._nodes.shape, fg._edges.shape)\n",
+        "    # print(fg2._nodes.shape, fg2._edges.shape)\n",
+        "    del g_gdf\n",
+        "    del out\n",
+        "    T1 = end1-start1\n",
+        "    print('\\nCPU',n_hop,'hop chain time:',np.round(T0,4),'\\nGPU',n_hop,'hop chain time:',np.round(T1,4),'\\nspeedup:', np.round(T0/T1,4))"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "rCsvQJa-6U0x",
+        "outputId": "70887aac-1bc8-499a-dc9e-40a1803e8fe3"
+      },
+      "execution_count": null,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "\n",
+            "CPU 1 hop chain time: 20.1676 \n",
+            "GPU 1 hop chain time: 1.0259 \n",
+            " 1 hop chain speedup: 19.6579\n",
+            "\n",
+            "CPU 2 hop chain time: 21.7168 \n",
+            "GPU 2 hop chain time: 2.2507 \n",
+            " 2 hop chain speedup: 9.6488\n",
+            "\n",
+            "CPU 8 hop chain time: 157.5035 \n",
+            "GPU 8 hop chain time: 7.8694 \n",
+            " 8 hop chain speedup: 20.0147\n"
+          ]
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "and similarly for these `hop` operations -- **10-40x** speed increases"
+      ],
+      "metadata": {
+        "id": "gHHhyYlzArjw"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "for n_hop in [1,2,8]:\n",
+        "    start_nodes = pd.DataFrame({g._node: [17116707]})\n",
+        "    start0 = time.time()\n",
+        "    for i in range(10):\n",
+        "      g2 = g.hop(\n",
+        "          nodes=start_nodes,\n",
+        "          direction='forward',\n",
+        "          hops=n_hop)\n",
+        "    end0 = time.time()\n",
+        "    T0 = end0-start0\n",
+        "    start_nodes = cudf.DataFrame({g._node: [17116707]})\n",
+        "    g_gdf = g.nodes(cudf.from_pandas(g._nodes)).edges(cudf.from_pandas(g._edges))\n",
+        "    start1 = time.time()\n",
+        "    for i in range(10):\n",
+        "        g2 = g_gdf.hop(\n",
+        "            nodes=start_nodes,\n",
+        "            direction='forward',\n",
+        "            hops=5)\n",
+        "    end1 = time.time()\n",
+        "    # print(fg._nodes.shape, fg._edges.shape)\n",
+        "    # print(fg2._nodes.shape, fg2._edges.shape)\n",
+        "    del start_nodes\n",
+        "    del g_gdf\n",
+        "    del g2\n",
+        "    T1 = end1-start1\n",
+        "    print('\\nCPU',n_hop,'hop chain time:',np.round(T0,4),'\\nGPU',n_hop,'hop chain time:',np.round(T1,4),'\\nspeedup:', np.round(T0/T1,4))"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "cnILbPnG7tf4",
+        "outputId": "bd4aa370-3b54-4c18-c92d-7aba957f658a"
+      },
+      "execution_count": null,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "\n",
+            "CPU 1 hop chain time: 12.3446 \n",
+            "GPU 1 hop chain time: 1.204 \n",
+            "speedup: 10.2526\n",
+            "\n",
+            "CPU 2 hop chain time: 13.2377 \n",
+            "GPU 2 hop chain time: 1.1608 \n",
+            "speedup: 11.4037\n",
+            "\n",
+            "CPU 8 hop chain time: 52.2491 \n",
+            "GPU 8 hop chain time: 1.2148 \n",
+            "speedup: 43.012\n"
+          ]
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "9dZzAAVONCD2"
+      },
+      "source": [
+        "<a name=\"gpl\"></a>\n",
+        "## GPlus\n",
+        "\n",
+        "- edges: 30494866\n",
+        "- nodes: 107614"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "-nhWGNekKpcZ",
+        "outputId": "0ce5e0c8-e5a4-4e8e-b595-3c544192bf24"
+      },
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "--2024-02-20 09:59:24--  https://snap.stanford.edu/data/gplus_combined.txt.gz\n",
+            "Resolving snap.stanford.edu (snap.stanford.edu)... 171.64.75.80\n",
+            "Connecting to snap.stanford.edu (snap.stanford.edu)|171.64.75.80|:443... connected.\n",
+            "HTTP request sent, awaiting response... 200 OK\n",
+            "Length: 398930514 (380M) [application/x-gzip]\n",
+            "Saving to: ‘gplus_combined.txt.gz’\n",
+            "\n",
+            "gplus_combined.txt. 100%[===================>] 380.45M  39.7MB/s    in 9.9s    \n",
+            "\n",
+            "2024-02-20 09:59:34 (38.5 MB/s) - ‘gplus_combined.txt.gz’ saved [398930514/398930514]\n",
+            "\n"
+          ]
+        }
+      ],
+      "source": [
+        "! wget https://snap.stanford.edu/data/gplus_combined.txt.gz"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "id": "g5wgA_c2KqwJ"
+      },
+      "outputs": [],
+      "source": [
+        "! gunzip gplus_combined.txt.gz"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "id": "52hgDbr0Kti6",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 260
+        },
+        "outputId": "1b81b614-f1b9-4031-db25-42ed9500c9c7"
+      },
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "(30494866, 2)\n",
+            "CPU times: user 16.8 s, sys: 1.41 s, total: 18.2 s\n",
+            "Wall time: 18.4 s\n"
+          ]
+        },
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "                       s                      d\n",
+              "0  116374117927631468606  101765416973555767821\n",
+              "1  112188647432305746617  107727150903234299458\n",
+              "2  116719211656774388392  100432456209427807893\n",
+              "3  117421021456205115327  101096322838605097368\n",
+              "4  116407635616074189669  113556266482860931616"
+            ],
+            "text/html": [
+              "\n",
+              "  <div id=\"df-37002e89-7515-49d9-996e-3ff42df86c6d\" class=\"colab-df-container\">\n",
+              "    <div>\n",
+              "<style scoped>\n",
+              "    .dataframe tbody tr th:only-of-type {\n",
+              "        vertical-align: middle;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe tbody tr th {\n",
+              "        vertical-align: top;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe thead th {\n",
+              "        text-align: right;\n",
+              "    }\n",
+              "</style>\n",
+              "<table border=\"1\" class=\"dataframe\">\n",
+              "  <thead>\n",
+              "    <tr style=\"text-align: right;\">\n",
+              "      <th></th>\n",
+              "      <th>s</th>\n",
+              "      <th>d</th>\n",
+              "    </tr>\n",
+              "  </thead>\n",
+              "  <tbody>\n",
+              "    <tr>\n",
+              "      <th>0</th>\n",
+              "      <td>116374117927631468606</td>\n",
+              "      <td>101765416973555767821</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>1</th>\n",
+              "      <td>112188647432305746617</td>\n",
+              "      <td>107727150903234299458</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>2</th>\n",
+              "      <td>116719211656774388392</td>\n",
+              "      <td>100432456209427807893</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>3</th>\n",
+              "      <td>117421021456205115327</td>\n",
+              "      <td>101096322838605097368</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>4</th>\n",
+              "      <td>116407635616074189669</td>\n",
+              "      <td>113556266482860931616</td>\n",
+              "    </tr>\n",
+              "  </tbody>\n",
+              "</table>\n",
+              "</div>\n",
+              "    <div class=\"colab-df-buttons\">\n",
+              "\n",
+              "  <div class=\"colab-df-container\">\n",
+              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-37002e89-7515-49d9-996e-3ff42df86c6d')\"\n",
+              "            title=\"Convert this dataframe to an interactive table.\"\n",
+              "            style=\"display:none;\">\n",
+              "\n",
+              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
+              "    <path d=\"M120-120v-720h720v720H120Zm60-500h600v-160H180v160Zm220 220h160v-160H400v160Zm0 220h160v-160H400v160ZM180-400h160v-160H180v160Zm440 0h160v-160H620v160ZM180-180h160v-160H180v160Zm440 0h160v-160H620v160Z\"/>\n",
+              "  </svg>\n",
+              "    </button>\n",
+              "\n",
+              "  <style>\n",
+              "    .colab-df-container {\n",
+              "      display:flex;\n",
+              "      gap: 12px;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-convert {\n",
+              "      background-color: #E8F0FE;\n",
+              "      border: none;\n",
+              "      border-radius: 50%;\n",
+              "      cursor: pointer;\n",
+              "      display: none;\n",
+              "      fill: #1967D2;\n",
+              "      height: 32px;\n",
+              "      padding: 0 0 0 0;\n",
+              "      width: 32px;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-convert:hover {\n",
+              "      background-color: #E2EBFA;\n",
+              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
+              "      fill: #174EA6;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-buttons div {\n",
+              "      margin-bottom: 4px;\n",
+              "    }\n",
+              "\n",
+              "    [theme=dark] .colab-df-convert {\n",
+              "      background-color: #3B4455;\n",
+              "      fill: #D2E3FC;\n",
+              "    }\n",
+              "\n",
+              "    [theme=dark] .colab-df-convert:hover {\n",
+              "      background-color: #434B5C;\n",
+              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
+              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
+              "      fill: #FFFFFF;\n",
+              "    }\n",
+              "  </style>\n",
+              "\n",
+              "    <script>\n",
+              "      const buttonEl =\n",
+              "        document.querySelector('#df-37002e89-7515-49d9-996e-3ff42df86c6d button.colab-df-convert');\n",
+              "      buttonEl.style.display =\n",
+              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
+              "\n",
+              "      async function convertToInteractive(key) {\n",
+              "        const element = document.querySelector('#df-37002e89-7515-49d9-996e-3ff42df86c6d');\n",
+              "        const dataTable =\n",
+              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
+              "                                                    [key], {});\n",
+              "        if (!dataTable) return;\n",
+              "\n",
+              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
+              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
+              "          + ' to learn more about interactive tables.';\n",
+              "        element.innerHTML = '';\n",
+              "        dataTable['output_type'] = 'display_data';\n",
+              "        await google.colab.output.renderOutput(dataTable, element);\n",
+              "        const docLink = document.createElement('div');\n",
+              "        docLink.innerHTML = docLinkHtml;\n",
+              "        element.appendChild(docLink);\n",
+              "      }\n",
+              "    </script>\n",
+              "  </div>\n",
+              "\n",
+              "\n",
+              "<div id=\"df-326e44f5-428e-4864-8700-ac2ce6e933f4\">\n",
+              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-326e44f5-428e-4864-8700-ac2ce6e933f4')\"\n",
+              "            title=\"Suggest charts\"\n",
+              "            style=\"display:none;\">\n",
+              "\n",
+              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
+              "     width=\"24px\">\n",
+              "    <g>\n",
+              "        <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
+              "    </g>\n",
+              "</svg>\n",
+              "  </button>\n",
+              "\n",
+              "<style>\n",
+              "  .colab-df-quickchart {\n",
+              "      --bg-color: #E8F0FE;\n",
+              "      --fill-color: #1967D2;\n",
+              "      --hover-bg-color: #E2EBFA;\n",
+              "      --hover-fill-color: #174EA6;\n",
+              "      --disabled-fill-color: #AAA;\n",
+              "      --disabled-bg-color: #DDD;\n",
+              "  }\n",
+              "\n",
+              "  [theme=dark] .colab-df-quickchart {\n",
+              "      --bg-color: #3B4455;\n",
+              "      --fill-color: #D2E3FC;\n",
+              "      --hover-bg-color: #434B5C;\n",
+              "      --hover-fill-color: #FFFFFF;\n",
+              "      --disabled-bg-color: #3B4455;\n",
+              "      --disabled-fill-color: #666;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart {\n",
+              "    background-color: var(--bg-color);\n",
+              "    border: none;\n",
+              "    border-radius: 50%;\n",
+              "    cursor: pointer;\n",
+              "    display: none;\n",
+              "    fill: var(--fill-color);\n",
+              "    height: 32px;\n",
+              "    padding: 0;\n",
+              "    width: 32px;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart:hover {\n",
+              "    background-color: var(--hover-bg-color);\n",
+              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
+              "    fill: var(--button-hover-fill-color);\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart-complete:disabled,\n",
+              "  .colab-df-quickchart-complete:disabled:hover {\n",
+              "    background-color: var(--disabled-bg-color);\n",
+              "    fill: var(--disabled-fill-color);\n",
+              "    box-shadow: none;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-spinner {\n",
+              "    border: 2px solid var(--fill-color);\n",
+              "    border-color: transparent;\n",
+              "    border-bottom-color: var(--fill-color);\n",
+              "    animation:\n",
+              "      spin 1s steps(1) infinite;\n",
+              "  }\n",
+              "\n",
+              "  @keyframes spin {\n",
+              "    0% {\n",
+              "      border-color: transparent;\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "      border-left-color: var(--fill-color);\n",
+              "    }\n",
+              "    20% {\n",
+              "      border-color: transparent;\n",
+              "      border-left-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "    }\n",
+              "    30% {\n",
+              "      border-color: transparent;\n",
+              "      border-left-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "      border-right-color: var(--fill-color);\n",
+              "    }\n",
+              "    40% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "    }\n",
+              "    60% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "    }\n",
+              "    80% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "    }\n",
+              "    90% {\n",
+              "      border-color: transparent;\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "    }\n",
+              "  }\n",
+              "</style>\n",
+              "\n",
+              "  <script>\n",
+              "    async function quickchart(key) {\n",
+              "      const quickchartButtonEl =\n",
+              "        document.querySelector('#' + key + ' button');\n",
+              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
+              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
+              "      try {\n",
+              "        const charts = await google.colab.kernel.invokeFunction(\n",
+              "            'suggestCharts', [key], {});\n",
+              "      } catch (error) {\n",
+              "        console.error('Error during call to suggestCharts:', error);\n",
+              "      }\n",
+              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
+              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
+              "    }\n",
+              "    (() => {\n",
+              "      let quickchartButtonEl =\n",
+              "        document.querySelector('#df-326e44f5-428e-4864-8700-ac2ce6e933f4 button');\n",
+              "      quickchartButtonEl.style.display =\n",
+              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
+              "    })();\n",
+              "  </script>\n",
+              "</div>\n",
+              "    </div>\n",
+              "  </div>\n"
+            ],
+            "application/vnd.google.colaboratory.intrinsic+json": {
+              "type": "dataframe",
+              "summary": "{\n  \"name\": \"get_ipython()\",\n  \"rows\": 5,\n  \"fields\": [\n    {\n      \"column\": \"s\",\n      \"properties\": {\n        \"dtype\": \"string\",\n        \"samples\": [\n          \"112188647432305746617\",\n          \"116407635616074189669\",\n          \"116719211656774388392\"\n        ],\n        \"num_unique_values\": 5,\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"d\",\n      \"properties\": {\n        \"dtype\": \"string\",\n        \"samples\": [\n          \"107727150903234299458\",\n          \"113556266482860931616\",\n          \"100432456209427807893\"\n        ],\n        \"num_unique_values\": 5,\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
+            }
+          },
+          "metadata": {},
+          "execution_count": 41
+        }
+      ],
+      "source": [
+        "%%time\n",
+        "ge_df = pd.read_csv('gplus_combined.txt', sep=' ', names=['s', 'd'])\n",
+        "print(ge_df.shape)\n",
+        "ge_df.head(5)"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "id": "w5YkN-nLK6UV",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 260
+        },
+        "outputId": "9c818e80-34b1-431a-d965-3305b45c1bb2"
+      },
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "(30494866, 2) (107614, 1)\n",
+            "CPU times: user 4.41 s, sys: 1.29 s, total: 5.7 s\n",
+            "Wall time: 5.69 s\n"
+          ]
+        },
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "                      id\n",
+              "0  116374117927631468606\n",
+              "1  112188647432305746617\n",
+              "2  116719211656774388392\n",
+              "3  117421021456205115327\n",
+              "4  116407635616074189669"
+            ],
+            "text/html": [
+              "\n",
+              "  <div id=\"df-18b91552-c868-4cde-8c8f-cef30e769b69\" class=\"colab-df-container\">\n",
+              "    <div>\n",
+              "<style scoped>\n",
+              "    .dataframe tbody tr th:only-of-type {\n",
+              "        vertical-align: middle;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe tbody tr th {\n",
+              "        vertical-align: top;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe thead th {\n",
+              "        text-align: right;\n",
+              "    }\n",
+              "</style>\n",
+              "<table border=\"1\" class=\"dataframe\">\n",
+              "  <thead>\n",
+              "    <tr style=\"text-align: right;\">\n",
+              "      <th></th>\n",
+              "      <th>id</th>\n",
+              "    </tr>\n",
+              "  </thead>\n",
+              "  <tbody>\n",
+              "    <tr>\n",
+              "      <th>0</th>\n",
+              "      <td>116374117927631468606</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>1</th>\n",
+              "      <td>112188647432305746617</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>2</th>\n",
+              "      <td>116719211656774388392</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>3</th>\n",
+              "      <td>117421021456205115327</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>4</th>\n",
+              "      <td>116407635616074189669</td>\n",
+              "    </tr>\n",
+              "  </tbody>\n",
+              "</table>\n",
+              "</div>\n",
+              "    <div class=\"colab-df-buttons\">\n",
+              "\n",
+              "  <div class=\"colab-df-container\">\n",
+              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-18b91552-c868-4cde-8c8f-cef30e769b69')\"\n",
+              "            title=\"Convert this dataframe to an interactive table.\"\n",
+              "            style=\"display:none;\">\n",
+              "\n",
+              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
+              "    <path d=\"M120-120v-720h720v720H120Zm60-500h600v-160H180v160Zm220 220h160v-160H400v160Zm0 220h160v-160H400v160ZM180-400h160v-160H180v160Zm440 0h160v-160H620v160ZM180-180h160v-160H180v160Zm440 0h160v-160H620v160Z\"/>\n",
+              "  </svg>\n",
+              "    </button>\n",
+              "\n",
+              "  <style>\n",
+              "    .colab-df-container {\n",
+              "      display:flex;\n",
+              "      gap: 12px;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-convert {\n",
+              "      background-color: #E8F0FE;\n",
+              "      border: none;\n",
+              "      border-radius: 50%;\n",
+              "      cursor: pointer;\n",
+              "      display: none;\n",
+              "      fill: #1967D2;\n",
+              "      height: 32px;\n",
+              "      padding: 0 0 0 0;\n",
+              "      width: 32px;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-convert:hover {\n",
+              "      background-color: #E2EBFA;\n",
+              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
+              "      fill: #174EA6;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-buttons div {\n",
+              "      margin-bottom: 4px;\n",
+              "    }\n",
+              "\n",
+              "    [theme=dark] .colab-df-convert {\n",
+              "      background-color: #3B4455;\n",
+              "      fill: #D2E3FC;\n",
+              "    }\n",
+              "\n",
+              "    [theme=dark] .colab-df-convert:hover {\n",
+              "      background-color: #434B5C;\n",
+              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
+              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
+              "      fill: #FFFFFF;\n",
+              "    }\n",
+              "  </style>\n",
+              "\n",
+              "    <script>\n",
+              "      const buttonEl =\n",
+              "        document.querySelector('#df-18b91552-c868-4cde-8c8f-cef30e769b69 button.colab-df-convert');\n",
+              "      buttonEl.style.display =\n",
+              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
+              "\n",
+              "      async function convertToInteractive(key) {\n",
+              "        const element = document.querySelector('#df-18b91552-c868-4cde-8c8f-cef30e769b69');\n",
+              "        const dataTable =\n",
+              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
+              "                                                    [key], {});\n",
+              "        if (!dataTable) return;\n",
+              "\n",
+              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
+              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
+              "          + ' to learn more about interactive tables.';\n",
+              "        element.innerHTML = '';\n",
+              "        dataTable['output_type'] = 'display_data';\n",
+              "        await google.colab.output.renderOutput(dataTable, element);\n",
+              "        const docLink = document.createElement('div');\n",
+              "        docLink.innerHTML = docLinkHtml;\n",
+              "        element.appendChild(docLink);\n",
+              "      }\n",
+              "    </script>\n",
+              "  </div>\n",
+              "\n",
+              "\n",
+              "<div id=\"df-164b8618-a7e8-4900-b561-e308fc38c946\">\n",
+              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-164b8618-a7e8-4900-b561-e308fc38c946')\"\n",
+              "            title=\"Suggest charts\"\n",
+              "            style=\"display:none;\">\n",
+              "\n",
+              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
+              "     width=\"24px\">\n",
+              "    <g>\n",
+              "        <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
+              "    </g>\n",
+              "</svg>\n",
+              "  </button>\n",
+              "\n",
+              "<style>\n",
+              "  .colab-df-quickchart {\n",
+              "      --bg-color: #E8F0FE;\n",
+              "      --fill-color: #1967D2;\n",
+              "      --hover-bg-color: #E2EBFA;\n",
+              "      --hover-fill-color: #174EA6;\n",
+              "      --disabled-fill-color: #AAA;\n",
+              "      --disabled-bg-color: #DDD;\n",
+              "  }\n",
+              "\n",
+              "  [theme=dark] .colab-df-quickchart {\n",
+              "      --bg-color: #3B4455;\n",
+              "      --fill-color: #D2E3FC;\n",
+              "      --hover-bg-color: #434B5C;\n",
+              "      --hover-fill-color: #FFFFFF;\n",
+              "      --disabled-bg-color: #3B4455;\n",
+              "      --disabled-fill-color: #666;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart {\n",
+              "    background-color: var(--bg-color);\n",
+              "    border: none;\n",
+              "    border-radius: 50%;\n",
+              "    cursor: pointer;\n",
+              "    display: none;\n",
+              "    fill: var(--fill-color);\n",
+              "    height: 32px;\n",
+              "    padding: 0;\n",
+              "    width: 32px;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart:hover {\n",
+              "    background-color: var(--hover-bg-color);\n",
+              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
+              "    fill: var(--button-hover-fill-color);\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart-complete:disabled,\n",
+              "  .colab-df-quickchart-complete:disabled:hover {\n",
+              "    background-color: var(--disabled-bg-color);\n",
+              "    fill: var(--disabled-fill-color);\n",
+              "    box-shadow: none;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-spinner {\n",
+              "    border: 2px solid var(--fill-color);\n",
+              "    border-color: transparent;\n",
+              "    border-bottom-color: var(--fill-color);\n",
+              "    animation:\n",
+              "      spin 1s steps(1) infinite;\n",
+              "  }\n",
+              "\n",
+              "  @keyframes spin {\n",
+              "    0% {\n",
+              "      border-color: transparent;\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "      border-left-color: var(--fill-color);\n",
+              "    }\n",
+              "    20% {\n",
+              "      border-color: transparent;\n",
+              "      border-left-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "    }\n",
+              "    30% {\n",
+              "      border-color: transparent;\n",
+              "      border-left-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "      border-right-color: var(--fill-color);\n",
+              "    }\n",
+              "    40% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "    }\n",
+              "    60% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "    }\n",
+              "    80% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "    }\n",
+              "    90% {\n",
+              "      border-color: transparent;\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "    }\n",
+              "  }\n",
+              "</style>\n",
+              "\n",
+              "  <script>\n",
+              "    async function quickchart(key) {\n",
+              "      const quickchartButtonEl =\n",
+              "        document.querySelector('#' + key + ' button');\n",
+              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
+              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
+              "      try {\n",
+              "        const charts = await google.colab.kernel.invokeFunction(\n",
+              "            'suggestCharts', [key], {});\n",
+              "      } catch (error) {\n",
+              "        console.error('Error during call to suggestCharts:', error);\n",
+              "      }\n",
+              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
+              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
+              "    }\n",
+              "    (() => {\n",
+              "      let quickchartButtonEl =\n",
+              "        document.querySelector('#df-164b8618-a7e8-4900-b561-e308fc38c946 button');\n",
+              "      quickchartButtonEl.style.display =\n",
+              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
+              "    })();\n",
+              "  </script>\n",
+              "</div>\n",
+              "    </div>\n",
+              "  </div>\n"
+            ],
+            "application/vnd.google.colaboratory.intrinsic+json": {
+              "type": "dataframe",
+              "summary": "{\n  \"name\": \"get_ipython()\",\n  \"rows\": 5,\n  \"fields\": [\n    {\n      \"column\": \"id\",\n      \"properties\": {\n        \"dtype\": \"string\",\n        \"samples\": [\n          \"112188647432305746617\",\n          \"116407635616074189669\",\n          \"116719211656774388392\"\n        ],\n        \"num_unique_values\": 5,\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
+            }
+          },
+          "metadata": {},
+          "execution_count": 42
+        }
+      ],
+      "source": [
+        "%%time\n",
+        "gg = graphistry.edges(ge_df, 's', 'd').materialize_nodes()\n",
+        "gg = graphistry.edges(ge_df, 's', 'd').nodes(gg._nodes, 'id')\n",
+        "print(gg._edges.shape, gg._nodes.shape)\n",
+        "gg._nodes.head(5)"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "id": "NKtz54uELX-8",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 116
+        },
+        "outputId": "aaccd673-85c1-40a4-ccdc-f13388e7a01a"
+      },
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "CPU times: user 471 ms, sys: 307 ms, total: 779 ms\n",
+            "Wall time: 776 ms\n"
+          ]
+        },
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "                      id\n",
+              "0  116374117927631468606"
+            ],
+            "text/html": [
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+              "    <div>\n",
+              "<style scoped>\n",
+              "    .dataframe tbody tr th:only-of-type {\n",
+              "        vertical-align: middle;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe tbody tr th {\n",
+              "        vertical-align: top;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe thead th {\n",
+              "        text-align: right;\n",
+              "    }\n",
+              "</style>\n",
+              "<table border=\"1\" class=\"dataframe\">\n",
+              "  <thead>\n",
+              "    <tr style=\"text-align: right;\">\n",
+              "      <th></th>\n",
+              "      <th>id</th>\n",
+              "    </tr>\n",
+              "  </thead>\n",
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+              "    <tr>\n",
+              "      <th>0</th>\n",
+              "      <td>116374117927631468606</td>\n",
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+              "  </tbody>\n",
+              "</table>\n",
+              "</div>\n",
+              "    <div class=\"colab-df-buttons\">\n",
+              "\n",
+              "  <div class=\"colab-df-container\">\n",
+              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-9891edfd-d16e-4aae-953d-3763664284ff')\"\n",
+              "            title=\"Convert this dataframe to an interactive table.\"\n",
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+              "  </svg>\n",
+              "    </button>\n",
+              "\n",
+              "  <style>\n",
+              "    .colab-df-container {\n",
+              "      display:flex;\n",
+              "      gap: 12px;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-convert {\n",
+              "      background-color: #E8F0FE;\n",
+              "      border: none;\n",
+              "      border-radius: 50%;\n",
+              "      cursor: pointer;\n",
+              "      display: none;\n",
+              "      fill: #1967D2;\n",
+              "      height: 32px;\n",
+              "      padding: 0 0 0 0;\n",
+              "      width: 32px;\n",
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+              "\n",
+              "    .colab-df-convert:hover {\n",
+              "      background-color: #E2EBFA;\n",
+              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
+              "      fill: #174EA6;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-buttons div {\n",
+              "      margin-bottom: 4px;\n",
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+              "\n",
+              "    [theme=dark] .colab-df-convert {\n",
+              "      background-color: #3B4455;\n",
+              "      fill: #D2E3FC;\n",
+              "    }\n",
+              "\n",
+              "    [theme=dark] .colab-df-convert:hover {\n",
+              "      background-color: #434B5C;\n",
+              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
+              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
+              "      fill: #FFFFFF;\n",
+              "    }\n",
+              "  </style>\n",
+              "\n",
+              "    <script>\n",
+              "      const buttonEl =\n",
+              "        document.querySelector('#df-9891edfd-d16e-4aae-953d-3763664284ff button.colab-df-convert');\n",
+              "      buttonEl.style.display =\n",
+              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
+              "\n",
+              "      async function convertToInteractive(key) {\n",
+              "        const element = document.querySelector('#df-9891edfd-d16e-4aae-953d-3763664284ff');\n",
+              "        const dataTable =\n",
+              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
+              "                                                    [key], {});\n",
+              "        if (!dataTable) return;\n",
+              "\n",
+              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
+              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
+              "          + ' to learn more about interactive tables.';\n",
+              "        element.innerHTML = '';\n",
+              "        dataTable['output_type'] = 'display_data';\n",
+              "        await google.colab.output.renderOutput(dataTable, element);\n",
+              "        const docLink = document.createElement('div');\n",
+              "        docLink.innerHTML = docLinkHtml;\n",
+              "        element.appendChild(docLink);\n",
+              "      }\n",
+              "    </script>\n",
+              "  </div>\n",
+              "\n",
+              "    </div>\n",
+              "  </div>\n"
+            ],
+            "application/vnd.google.colaboratory.intrinsic+json": {
+              "type": "dataframe",
+              "summary": "{\n  \"name\": \"get_ipython()\",\n  \"rows\": 1,\n  \"fields\": [\n    {\n      \"column\": \"id\",\n      \"properties\": {\n        \"dtype\": \"string\",\n        \"samples\": [\n          \"116374117927631468606\"\n        ],\n        \"num_unique_values\": 1,\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
+            }
+          },
+          "metadata": {},
+          "execution_count": 43
+        }
+      ],
+      "source": [
+        "%%time\n",
+        "gg.chain([ n({'id': '116374117927631468606'})])._nodes"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "on the GPlus data, simpler `chain` operations over several different hops -- **100-200x** speed increases"
+      ],
+      "metadata": {
+        "id": "e4ZchWvrBKdY"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "for n_hop in [1,2,3,4,5]:\n",
+        "    start_nodes = pd.DataFrame({fg._node: [0]})\n",
+        "    start0 = time.time()\n",
+        "    out = gg.chain([ n({'id': '116374117927631468606'}), e_forward(hops=n_hop)])._nodes\n",
+        "    end0 = time.time()\n",
+        "    T0 = end0-start0\n",
+        "    gg_gdf = gg.nodes(lambda g: cudf.DataFrame(g._nodes)).edges(lambda g: cudf.DataFrame(g._edges))\n",
+        "    start1 = time.time()\n",
+        "    out = gg_gdf.chain([ n({'id': '116374117927631468606'}), e_forward(hops=n_hop)])\n",
+        "    end1 = time.time()\n",
+        "    # print(fg._nodes.shape, fg._edges.shape)\n",
+        "    # print(fg2._nodes.shape, fg2._edges.shape)\n",
+        "    del gg_gdf\n",
+        "    del out\n",
+        "    T1 = end1-start1\n",
+        "    print('\\nCPU',n_hop,'hop chain time:',np.round(T0,4),'\\nGPU',n_hop,'hop chain time:',np.round(T1,4),'\\nspeedup:', np.round(T0/T1,4))"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 507
+        },
+        "id": "fTnU8MLr8tV5",
+        "outputId": "40a2f455-9d79-4a3c-abeb-aac93713a424"
+      },
+      "execution_count": null,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "\n",
+            "CPU 1 hop chain time: 70.7013 \n",
+            "GPU 1 hop chain time: 0.2911 \n",
+            "speedup: 242.9049\n",
+            "\n",
+            "CPU 2 hop chain time: 84.2395 \n",
+            "GPU 2 hop chain time: 0.6138 \n",
+            "speedup: 137.252\n"
+          ]
+        },
+        {
+          "output_type": "error",
+          "ename": "KeyboardInterrupt",
+          "evalue": "",
+          "traceback": [
+            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+            "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
+            "\u001b[0;32m<ipython-input-46-c29c7daea5b2>\u001b[0m in \u001b[0;36m<cell line: 1>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      2\u001b[0m     \u001b[0mstart_nodes\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpd\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mDataFrame\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m{\u001b[0m\u001b[0mfg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_node\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m     \u001b[0mstart0\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtime\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtime\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m     \u001b[0mout\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mgg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mchain\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m \u001b[0mn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m{\u001b[0m\u001b[0;34m'id'\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;34m'116374117927631468606'\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0me_forward\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mhops\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mn_hop\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_nodes\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      5\u001b[0m     \u001b[0mend0\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtime\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtime\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m     \u001b[0mT0\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mend0\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mstart0\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/graphistry/compute/ComputeMixin.py\u001b[0m in \u001b[0;36mchain\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n\u001b[1;32m    391\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    392\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mchain\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 393\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mchain_base\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    394\u001b[0m     \u001b[0mchain\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__doc__\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mchain_base\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__doc__\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/graphistry/compute/chain.py\u001b[0m in \u001b[0;36mchain\u001b[0;34m(self, ops, engine)\u001b[0m\n\u001b[1;32m    285\u001b[0m         )\n\u001b[1;32m    286\u001b[0m         g_step = (\n\u001b[0;32m--> 287\u001b[0;31m             op(\n\u001b[0m\u001b[1;32m    288\u001b[0m                 \u001b[0mg\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mg\u001b[0m\u001b[0;34m,\u001b[0m  \u001b[0;31m# transition via any original edge\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    289\u001b[0m                 \u001b[0mprev_node_wavefront\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mprev_step_nodes\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/graphistry/compute/ast.py\u001b[0m in \u001b[0;36m__call__\u001b[0;34m(self, g, prev_node_wavefront, target_wave_front, engine)\u001b[0m\n\u001b[1;32m    326\u001b[0m             \u001b[0mlogger\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdebug\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'----------------------------------------'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    327\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 328\u001b[0;31m         out_g = g.hop(\n\u001b[0m\u001b[1;32m    329\u001b[0m             \u001b[0mnodes\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mprev_node_wavefront\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    330\u001b[0m             \u001b[0mhops\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mhops\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/graphistry/compute/ComputeMixin.py\u001b[0m in \u001b[0;36mhop\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n\u001b[1;32m    379\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    380\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mhop\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 381\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mhop_base\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    382\u001b[0m     \u001b[0mhop\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__doc__\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mhop_base\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__doc__\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    383\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/graphistry/compute/hop.py\u001b[0m in \u001b[0;36mhop\u001b[0;34m(self, nodes, hops, to_fixed_point, direction, edge_match, source_node_match, destination_node_match, source_node_query, destination_node_query, edge_query, return_as_wave_front, target_wave_front, engine)\u001b[0m\n\u001b[1;32m    188\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mdirection\u001b[0m \u001b[0;32min\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m'forward'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'undirected'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    189\u001b[0m             hop_edges_forward = (\n\u001b[0;32m--> 190\u001b[0;31m                 wave_front_iter.merge(\n\u001b[0m\u001b[1;32m    191\u001b[0m                     \u001b[0medges_indexed\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mg2\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_source\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mg2\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_destination\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mEDGE_ID\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0massign\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;34m{\u001b[0m\u001b[0mg2\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_node\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0medges_indexed\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mg2\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_source\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    192\u001b[0m                     \u001b[0mhow\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'inner'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/pandas/core/frame.py\u001b[0m in \u001b[0;36mmerge\u001b[0;34m(self, right, how, on, left_on, right_on, left_index, right_index, sort, suffixes, copy, indicator, validate)\u001b[0m\n\u001b[1;32m  10091\u001b[0m         \u001b[0;32mfrom\u001b[0m \u001b[0mpandas\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcore\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreshape\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmerge\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mmerge\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m  10092\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m> 10093\u001b[0;31m         return merge(\n\u001b[0m\u001b[1;32m  10094\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m  10095\u001b[0m             \u001b[0mright\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/pandas/core/reshape/merge.py\u001b[0m in \u001b[0;36mmerge\u001b[0;34m(left, right, how, on, left_on, right_on, left_index, right_index, sort, suffixes, copy, indicator, validate)\u001b[0m\n\u001b[1;32m    122\u001b[0m         \u001b[0mvalidate\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mvalidate\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    123\u001b[0m     )\n\u001b[0;32m--> 124\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mop\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_result\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcopy\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mcopy\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    125\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    126\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/pandas/core/reshape/merge.py\u001b[0m in \u001b[0;36mget_result\u001b[0;34m(self, copy)\u001b[0m\n\u001b[1;32m    771\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mleft\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mright\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_indicator_pre_merge\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mleft\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mright\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    772\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 773\u001b[0;31m         \u001b[0mjoin_index\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mleft_indexer\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mright_indexer\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_get_join_info\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    774\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    775\u001b[0m         result = self._reindex_and_concat(\n",
+            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/pandas/core/reshape/merge.py\u001b[0m in \u001b[0;36m_get_join_info\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m   1024\u001b[0m             )\n\u001b[1;32m   1025\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1026\u001b[0;31m             \u001b[0;34m(\u001b[0m\u001b[0mleft_indexer\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mright_indexer\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_get_join_indexers\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1027\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1028\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mright_index\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/pandas/core/reshape/merge.py\u001b[0m in \u001b[0;36m_get_join_indexers\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    998\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m_get_join_indexers\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m->\u001b[0m \u001b[0mtuple\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mnpt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mNDArray\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mintp\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnpt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mNDArray\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mintp\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    999\u001b[0m         \u001b[0;34m\"\"\"return the join indexers\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1000\u001b[0;31m         return get_join_indexers(\n\u001b[0m\u001b[1;32m   1001\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mleft_join_keys\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mright_join_keys\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msort\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msort\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhow\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mhow\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1002\u001b[0m         )\n",
+            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/pandas/core/reshape/merge.py\u001b[0m in \u001b[0;36mget_join_indexers\u001b[0;34m(left_keys, right_keys, sort, how, **kwargs)\u001b[0m\n\u001b[1;32m   1583\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mn\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mleft_keys\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1584\u001b[0m     )\n\u001b[0;32m-> 1585\u001b[0;31m     \u001b[0mzipped\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mzip\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mmapped\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1586\u001b[0m     \u001b[0mllab\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrlab\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mshape\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mlist\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mx\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mzipped\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1587\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/pandas/core/reshape/merge.py\u001b[0m in \u001b[0;36m<genexpr>\u001b[0;34m(.0)\u001b[0m\n\u001b[1;32m   1580\u001b[0m     \u001b[0;31m# get left & right join labels and num. of levels at each location\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1581\u001b[0m     mapped = (\n\u001b[0;32m-> 1582\u001b[0;31m         \u001b[0m_factorize_keys\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mleft_keys\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mright_keys\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msort\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0msort\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhow\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mhow\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1583\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mn\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mleft_keys\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1584\u001b[0m     )\n",
+            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/pandas/core/reshape/merge.py\u001b[0m in \u001b[0;36m_factorize_keys\u001b[0;34m(lk, rk, sort, how)\u001b[0m\n\u001b[1;32m   2331\u001b[0m     \u001b[0;31m# \"Union[ndarray[Any, dtype[signedinteger[_64Bit]]],\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2332\u001b[0m     \u001b[0;31m# ndarray[Any, dtype[object_]]]\"; expected \"ndarray[Any, dtype[object_]]\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2333\u001b[0;31m     \u001b[0mrlab\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mrizer\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfactorize\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrk\u001b[0m\u001b[0;34m)\u001b[0m  \u001b[0;31m# type: ignore[arg-type]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   2334\u001b[0m     \u001b[0;32massert\u001b[0m \u001b[0mllab\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdtype\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdtype\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mintp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mllab\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdtype\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2335\u001b[0m     \u001b[0;32massert\u001b[0m \u001b[0mrlab\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdtype\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdtype\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mintp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrlab\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdtype\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+            "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
+          ]
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "and similarly for these hop operations -- **100x** speed increases"
+      ],
+      "metadata": {
+        "id": "80bs6Y5pBWb2"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "for n_hop in [1,2,3,4,5]:\n",
+        "    start_nodes = pd.DataFrame({gg._node: ['116374117927631468606']})\n",
+        "    start0 = time.time()\n",
+        "    for i in range(1):\n",
+        "      g2 = gg.hop(\n",
+        "          nodes=start_nodes,\n",
+        "          direction='forward',\n",
+        "          hops=n_hop)\n",
+        "    end0 = time.time()\n",
+        "    T0 = end0-start0\n",
+        "    start_nodes = cudf.DataFrame({gg._node: ['116374117927631468606']})\n",
+        "    gg_gdf = gg.nodes(cudf.from_pandas(gg._nodes)).edges(cudf.from_pandas(gg._edges))\n",
+        "    start1 = time.time()\n",
+        "    for i in range(1):\n",
+        "      g2 = gg_gdf.hop(\n",
+        "          nodes=start_nodes,\n",
+        "          direction='forward',\n",
+        "          hops=n_hop)\n",
+        "    end1 = time.time()\n",
+        "    # print(fg._nodes.shape, fg._edges.shape)\n",
+        "    # print(fg2._nodes.shape, fg2._edges.shape)\n",
+        "    del start_nodes\n",
+        "    del gg_gdf\n",
+        "    del g2\n",
+        "    T1 = end1-start1\n",
+        "    print('\\nCPU',n_hop,'hop chain time:',np.round(T0,4),'\\nGPU',n_hop,'hop chain time:',np.round(T1,4),'\\nspeedup:', np.round(T0/T1,4))"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "N2-gDFod9vc3",
+        "outputId": "c6967f1f-fa01-41a6-a776-02e2892f300f"
+      },
+      "execution_count": null,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "\n",
+            "CPU 1 hop chain time: 38.0714 \n",
+            "GPU 1 hop chain time: 0.2615 \n",
+            "speedup: 145.5678\n",
+            "\n",
+            "CPU 2 hop chain time: 52.949 \n",
+            "GPU 2 hop chain time: 0.4553 \n",
+            "speedup: 116.2876\n"
+          ]
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "R03M_swxarKC"
+      },
+      "source": [
+        "<a name=\"ork\"></a>\n",
+        "## Orkut\n",
+        "- 117M edges\n",
+        "- 3M nodes"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "id": "QoabYR2maxPo",
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "outputId": "f58e2837-9417-490b-882c-b1f478ed53f8"
+      },
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "--2024-02-19 06:02:00--  https://snap.stanford.edu/data/bigdata/communities/com-orkut.ungraph.txt.gz\n",
+            "Resolving snap.stanford.edu (snap.stanford.edu)... 171.64.75.80\n",
+            "Connecting to snap.stanford.edu (snap.stanford.edu)|171.64.75.80|:443... connected.\n",
+            "HTTP request sent, awaiting response... 200 OK\n",
+            "Length: 447251958 (427M) [application/x-gzip]\n",
+            "Saving to: ‘com-orkut.ungraph.txt.gz’\n",
+            "\n",
+            "com-orkut.ungraph.t 100%[===================>] 426.53M  31.8MB/s    in 11s     \n",
+            "\n",
+            "2024-02-19 06:02:11 (37.4 MB/s) - ‘com-orkut.ungraph.txt.gz’ saved [447251958/447251958]\n",
+            "\n"
+          ]
+        }
+      ],
+      "source": [
+        "! wget https://snap.stanford.edu/data/bigdata/communities/com-orkut.ungraph.txt.gz"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "id": "BvvfFPKWbAVJ"
+      },
+      "outputs": [],
+      "source": [
+        "! gunzip com-orkut.ungraph.txt.gz"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "id": "YsWwRoPqbPIb",
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "outputId": "5c12501a-e724-44d5-f651-e1860a8638af"
+      },
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "# Undirected graph: ../../data/output/orkut.txt\n",
+            "# Orkut\n",
+            "# Nodes: 3072441 Edges: 117185083\n",
+            "# FromNodeId\tToNodeId\n",
+            "1\t2\n",
+            "1\t3\n",
+            "1\t4\n"
+          ]
+        }
+      ],
+      "source": [
+        "! head -n 7 com-orkut.ungraph.txt"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "id": "cbMC8r2ldjbW",
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "outputId": "87ee2818-72d9-46e7-d0d8-5d16958e10c8"
+      },
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "('24.02.01', '0.33.0')"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 8
+        }
+      ],
+      "source": [
+        "import pandas as pd\n",
+        "\n",
+        "import graphistry\n",
+        "\n",
+        "from graphistry import (\n",
+        "\n",
+        "    # graph operators\n",
+        "    n, e_undirected, e_forward, e_reverse,\n",
+        "\n",
+        "    # attribute predicates\n",
+        "    is_in, ge, startswith, contains, match as match_re\n",
+        ")\n",
+        "\n",
+        "import cudf\n",
+        "\n",
+        "#work around google colab shell encoding bugs\n",
+        "import locale\n",
+        "locale.getpreferredencoding = lambda: \"UTF-8\"\n",
+        "\n",
+        "cudf.__version__, graphistry.__version__"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "id": "TopFxAvnh_Cv",
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "outputId": "52288638-691e-47e4-87fc-4f761a3e9302"
+      },
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "Mon Feb 19 06:02:29 2024       \n",
+            "+---------------------------------------------------------------------------------------+\n",
+            "| NVIDIA-SMI 535.104.05             Driver Version: 535.104.05   CUDA Version: 12.2     |\n",
+            "|-----------------------------------------+----------------------+----------------------+\n",
+            "| GPU  Name                 Persistence-M | Bus-Id        Disp.A | Volatile Uncorr. ECC |\n",
+            "| Fan  Temp   Perf          Pwr:Usage/Cap |         Memory-Usage | GPU-Util  Compute M. |\n",
+            "|                                         |                      |               MIG M. |\n",
+            "|=========================================+======================+======================|\n",
+            "|   0  Tesla T4                       Off | 00000000:00:04.0 Off |                    0 |\n",
+            "| N/A   64C    P0              29W /  70W |    111MiB / 15360MiB |      0%      Default |\n",
+            "|                                         |                      |                  N/A |\n",
+            "+-----------------------------------------+----------------------+----------------------+\n",
+            "                                                                                         \n",
+            "+---------------------------------------------------------------------------------------+\n",
+            "| Processes:                                                                            |\n",
+            "|  GPU   GI   CI        PID   Type   Process name                            GPU Memory |\n",
+            "|        ID   ID                                                             Usage      |\n",
+            "|=======================================================================================|\n",
+            "+---------------------------------------------------------------------------------------+\n"
+          ]
+        }
+      ],
+      "source": [
+        "! nvidia-smi"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "id": "Oczs87ITbJgw",
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "outputId": "b894db9b-13d1-426a-b162-dea780abce3b"
+      },
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "(117185082, 2)\n",
+            "   s  d\n",
+            "0  1  3\n",
+            "1  1  4\n",
+            "2  1  5\n",
+            "3  1  6\n",
+            "4  1  7\n",
+            "s    int64\n",
+            "d    int64\n",
+            "dtype: object\n",
+            "CPU times: user 2.34 s, sys: 1.29 s, total: 3.63 s\n",
+            "Wall time: 3.77 s\n"
+          ]
+        }
+      ],
+      "source": [
+        "%%time\n",
+        "co_df = cudf.read_csv('com-orkut.ungraph.txt', sep='\\t', names=['s', 'd'], skiprows=5).to_pandas()\n",
+        "print(co_df.shape)\n",
+        "print(co_df.head(5))\n",
+        "print(co_df.dtypes)\n",
+        "#del co_df"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "from load into gpu and back to cpu again"
+      ],
+      "metadata": {
+        "id": "2QLDI3vdAtkf"
+      }
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "id": "gGSDjTtveFAT",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 260
+        },
+        "outputId": "d8501df9-7070-4bfa-c5e2-49a581df5f56"
+      },
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "(3072441, 1) (117185082, 2)\n",
+            "CPU times: user 2.06 s, sys: 7.93 s, total: 10 s\n",
+            "Wall time: 11.2 s\n"
+          ]
+        },
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "   id\n",
+              "0   1\n",
+              "1   2\n",
+              "2   3\n",
+              "3   4\n",
+              "4   5"
+            ],
+            "text/html": [
+              "\n",
+              "  <div id=\"df-1a654a77-93b5-4de8-97a3-bf1bbd1acda7\" class=\"colab-df-container\">\n",
+              "    <div>\n",
+              "<style scoped>\n",
+              "    .dataframe tbody tr th:only-of-type {\n",
+              "        vertical-align: middle;\n",
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+              "\n",
+              "    .dataframe tbody tr th {\n",
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+              "    .dataframe thead th {\n",
+              "        text-align: right;\n",
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+              "</style>\n",
+              "<table border=\"1\" class=\"dataframe\">\n",
+              "  <thead>\n",
+              "    <tr style=\"text-align: right;\">\n",
+              "      <th></th>\n",
+              "      <th>id</th>\n",
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+              "  </thead>\n",
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+              "    <tr>\n",
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+              "      <th>3</th>\n",
+              "      <td>4</td>\n",
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+              "      <th>4</th>\n",
+              "      <td>5</td>\n",
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+              "</div>\n",
+              "    <div class=\"colab-df-buttons\">\n",
+              "\n",
+              "  <div class=\"colab-df-container\">\n",
+              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-1a654a77-93b5-4de8-97a3-bf1bbd1acda7')\"\n",
+              "            title=\"Convert this dataframe to an interactive table.\"\n",
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+              "  </svg>\n",
+              "    </button>\n",
+              "\n",
+              "  <style>\n",
+              "    .colab-df-container {\n",
+              "      display:flex;\n",
+              "      gap: 12px;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-convert {\n",
+              "      background-color: #E8F0FE;\n",
+              "      border: none;\n",
+              "      border-radius: 50%;\n",
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+              "    .colab-df-convert:hover {\n",
+              "      background-color: #E2EBFA;\n",
+              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
+              "      fill: #174EA6;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-buttons div {\n",
+              "      margin-bottom: 4px;\n",
+              "    }\n",
+              "\n",
+              "    [theme=dark] .colab-df-convert {\n",
+              "      background-color: #3B4455;\n",
+              "      fill: #D2E3FC;\n",
+              "    }\n",
+              "\n",
+              "    [theme=dark] .colab-df-convert:hover {\n",
+              "      background-color: #434B5C;\n",
+              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
+              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
+              "      fill: #FFFFFF;\n",
+              "    }\n",
+              "  </style>\n",
+              "\n",
+              "    <script>\n",
+              "      const buttonEl =\n",
+              "        document.querySelector('#df-1a654a77-93b5-4de8-97a3-bf1bbd1acda7 button.colab-df-convert');\n",
+              "      buttonEl.style.display =\n",
+              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
+              "\n",
+              "      async function convertToInteractive(key) {\n",
+              "        const element = document.querySelector('#df-1a654a77-93b5-4de8-97a3-bf1bbd1acda7');\n",
+              "        const dataTable =\n",
+              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
+              "                                                    [key], {});\n",
+              "        if (!dataTable) return;\n",
+              "\n",
+              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
+              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
+              "          + ' to learn more about interactive tables.';\n",
+              "        element.innerHTML = '';\n",
+              "        dataTable['output_type'] = 'display_data';\n",
+              "        await google.colab.output.renderOutput(dataTable, element);\n",
+              "        const docLink = document.createElement('div');\n",
+              "        docLink.innerHTML = docLinkHtml;\n",
+              "        element.appendChild(docLink);\n",
+              "      }\n",
+              "    </script>\n",
+              "  </div>\n",
+              "\n",
+              "\n",
+              "<div id=\"df-81e3ded9-c90b-4696-9661-cffe40b3414c\">\n",
+              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-81e3ded9-c90b-4696-9661-cffe40b3414c')\"\n",
+              "            title=\"Suggest charts\"\n",
+              "            style=\"display:none;\">\n",
+              "\n",
+              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
+              "     width=\"24px\">\n",
+              "    <g>\n",
+              "        <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
+              "    </g>\n",
+              "</svg>\n",
+              "  </button>\n",
+              "\n",
+              "<style>\n",
+              "  .colab-df-quickchart {\n",
+              "      --bg-color: #E8F0FE;\n",
+              "      --fill-color: #1967D2;\n",
+              "      --hover-bg-color: #E2EBFA;\n",
+              "      --hover-fill-color: #174EA6;\n",
+              "      --disabled-fill-color: #AAA;\n",
+              "      --disabled-bg-color: #DDD;\n",
+              "  }\n",
+              "\n",
+              "  [theme=dark] .colab-df-quickchart {\n",
+              "      --bg-color: #3B4455;\n",
+              "      --fill-color: #D2E3FC;\n",
+              "      --hover-bg-color: #434B5C;\n",
+              "      --hover-fill-color: #FFFFFF;\n",
+              "      --disabled-bg-color: #3B4455;\n",
+              "      --disabled-fill-color: #666;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart {\n",
+              "    background-color: var(--bg-color);\n",
+              "    border: none;\n",
+              "    border-radius: 50%;\n",
+              "    cursor: pointer;\n",
+              "    display: none;\n",
+              "    fill: var(--fill-color);\n",
+              "    height: 32px;\n",
+              "    padding: 0;\n",
+              "    width: 32px;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart:hover {\n",
+              "    background-color: var(--hover-bg-color);\n",
+              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
+              "    fill: var(--button-hover-fill-color);\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart-complete:disabled,\n",
+              "  .colab-df-quickchart-complete:disabled:hover {\n",
+              "    background-color: var(--disabled-bg-color);\n",
+              "    fill: var(--disabled-fill-color);\n",
+              "    box-shadow: none;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-spinner {\n",
+              "    border: 2px solid var(--fill-color);\n",
+              "    border-color: transparent;\n",
+              "    border-bottom-color: var(--fill-color);\n",
+              "    animation:\n",
+              "      spin 1s steps(1) infinite;\n",
+              "  }\n",
+              "\n",
+              "  @keyframes spin {\n",
+              "    0% {\n",
+              "      border-color: transparent;\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "      border-left-color: var(--fill-color);\n",
+              "    }\n",
+              "    20% {\n",
+              "      border-color: transparent;\n",
+              "      border-left-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "    }\n",
+              "    30% {\n",
+              "      border-color: transparent;\n",
+              "      border-left-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "      border-right-color: var(--fill-color);\n",
+              "    }\n",
+              "    40% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "    }\n",
+              "    60% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "    }\n",
+              "    80% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "    }\n",
+              "    90% {\n",
+              "      border-color: transparent;\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "    }\n",
+              "  }\n",
+              "</style>\n",
+              "\n",
+              "  <script>\n",
+              "    async function quickchart(key) {\n",
+              "      const quickchartButtonEl =\n",
+              "        document.querySelector('#' + key + ' button');\n",
+              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
+              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
+              "      try {\n",
+              "        const charts = await google.colab.kernel.invokeFunction(\n",
+              "            'suggestCharts', [key], {});\n",
+              "      } catch (error) {\n",
+              "        console.error('Error during call to suggestCharts:', error);\n",
+              "      }\n",
+              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
+              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
+              "    }\n",
+              "    (() => {\n",
+              "      let quickchartButtonEl =\n",
+              "        document.querySelector('#df-81e3ded9-c90b-4696-9661-cffe40b3414c button');\n",
+              "      quickchartButtonEl.style.display =\n",
+              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
+              "    })();\n",
+              "  </script>\n",
+              "</div>\n",
+              "    </div>\n",
+              "  </div>\n"
+            ],
+            "application/vnd.google.colaboratory.intrinsic+json": {
+              "type": "dataframe",
+              "summary": "{\n  \"name\": \"get_ipython()\",\n  \"rows\": 5,\n  \"fields\": [\n    {\n      \"column\": \"id\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 1,\n        \"min\": 1,\n        \"max\": 5,\n        \"samples\": [\n          2,\n          5,\n          3\n        ],\n        \"num_unique_values\": 5,\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
+            }
+          },
+          "metadata": {},
+          "execution_count": 11
+        }
+      ],
+      "source": [
+        "%%time\n",
+        "co_g = graphistry.edges(cudf.DataFrame(co_df), 's', 'd').materialize_nodes(engine='cudf')\n",
+        "co_g = co_g.nodes(lambda g: g._nodes.to_pandas()).edges(lambda g: g._edges.to_pandas())\n",
+        "print(co_g._nodes.shape, co_g._edges.shape)\n",
+        "co_g._nodes.head(5)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "on the Orkut data, simpler chain operations over several different hops -- **10-50x** speed increases"
+      ],
+      "metadata": {
+        "id": "G4f19-djBd7J"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "for n_hop in [1,2,3,4,5,6]:\n",
+        "    start_nodes = pd.DataFrame({fg._node: [0]})\n",
+        "    start0 = time.time()\n",
+        "    for i in range(10):\n",
+        "        out = co_g.chain([ n({'id': 1}), e_forward(hops=n_hop)])._nodes\n",
+        "    end0 = time.time()\n",
+        "    T0 = end0-start0\n",
+        "    co_gdf = co_g.nodes(lambda g: cudf.DataFrame(g._nodes)).edges(lambda g: cudf.DataFrame(g._edges))\n",
+        "    start1 = time.time()\n",
+        "    for i in range(10):\n",
+        "        out = co_gdf.chain([ n({'id': 1}), e_forward(hops=n_hop)])    end1 = time.time()\n",
+        "    # print(fg._nodes.shape, fg._edges.shape)\n",
+        "    # print(fg2._nodes.shape, fg2._edges.shape)\n",
+        "    del co_gdf\n",
+        "    del out\n",
+        "    T1 = end1-start1\n",
+        "    print('\\nCPU',n_hop,'hop chain time:',np.round(T0,4),'\\nGPU',n_hop,'hop chain time:',np.round(T1,4),'\\nspeedup:', np.round(T0/T1,4))"
+      ],
+      "metadata": {
+        "id": "yWabsh_k-tgy"
+      },
+      "execution_count": null,
+      "outputs": []
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "and similarly for these hop operations -- 10-40x speed increases"
+      ],
+      "metadata": {
+        "id": "v-gVx5trBeSl"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "for n_hop in [1,2,3,4,5]:\n",
+        "    start_nodes = pd.DataFrame({'id': [1]})\n",
+        "    start0 = time.time()\n",
+        "    for i in range(1):\n",
+        "      g2 = co_g.hop(\n",
+        "          nodes=start_nodes,\n",
+        "          direction='forward',\n",
+        "          hops=n_hop)\n",
+        "    end0 = time.time()\n",
+        "    T0 = end0-start0\n",
+        "    start_nodes = cudf.DataFrame({'id': [1]})\n",
+        "    co_gdf = co_g.nodes(lambda g: cudf.DataFrame(g._nodes)).edges(lambda g: cudf.DataFrame(g._edges))\n",
+        "    start1 = time.time()\n",
+        "    for i in range(1):\n",
+        "      g2 = gg_gdf.hop(\n",
+        "          nodes=start_nodes,\n",
+        "          direction='forward',\n",
+        "          hops=n_hop)\n",
+        "    end1 = time.time()\n",
+        "    # print(fg._nodes.shape, fg._edges.shape)\n",
+        "    # print(fg2._nodes.shape, fg2._edges.shape)\n",
+        "    del start_nodes\n",
+        "    del co_gdf\n",
+        "    del g2\n",
+        "    T1 = end1-start1\n",
+        "    print('\\nCPU',n_hop,'hop chain time:',np.round(T0,4),'\\nGPU',n_hop,'hop chain time:',np.round(T1,4),'\\nspeedup:', np.round(T0/T1,4))"
+      ],
+      "metadata": {
+        "id": "kHZatWCB_qwd"
+      },
+      "execution_count": null,
+      "outputs": []
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "id": "eiXFImxF-rzw"
+      },
+      "outputs": [],
+      "source": [
+        "!lscpu\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "id": "wJohLi58-sN5",
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "outputId": "07a499d6-3109-486e-d387-002abd133d22"
+      },
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "               total        used        free      shared  buff/cache   available\n",
+            "Mem:            12Gi       5.8Gi       1.6Gi       1.0Gi       5.2Gi       5.5Gi\n",
+            "Swap:             0B          0B          0B\n"
+          ]
+        }
+      ],
+      "source": [
+        "!free -h\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "id": "Ygc2nrkznlCu"
+      },
+      "outputs": [],
+      "source": []
+    }
+  ],
+  "metadata": {
+    "accelerator": "GPU",
+    "colab": {
+      "gpuType": "T4",
+      "provenance": [],
+      "toc_visible": true,
+      "include_colab_link": true
+    },
+    "kernelspec": {
+      "display_name": "Python 3",
+      "name": "python3"
+    },
+    "language_info": {
+      "name": "python"
+    }
+  },
+  "nbformat": 4,
+  "nbformat_minor": 0
+}
\ No newline at end of file
diff --git a/demos/gfql/simple_gfql_notebook.ipynb b/demos/gfql/simple_gfql_notebook.ipynb
new file mode 100644
index 0000000000..5f27f7b619
--- /dev/null
+++ b/demos/gfql/simple_gfql_notebook.ipynb
@@ -0,0 +1,264 @@
+{
+  "nbformat": 4,
+  "nbformat_minor": 0,
+  "metadata": {
+    "colab": {
+      "provenance": [],
+      "gpuType": "T4",
+      "include_colab_link": true
+    },
+    "kernelspec": {
+      "name": "python3",
+      "display_name": "Python 3"
+    },
+    "language_info": {
+      "name": "python"
+    },
+    "accelerator": "GPU"
+  },
+  "cells": [
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "view-in-github",
+        "colab_type": "text"
+      },
+      "source": [
+        "<a href=\"https://colab.research.google.com/github/dcolinmorgan/grph/blob/main/simple_GFQL.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "# simple GFQL demo on Twitter data\n",
+        "\n",
+        "* Twitter\tNetwork with 81,306 Nodes\tand 2,420,766 Edges\n",
+        "\n",
+        "* The single-threaded CPU mode benefits from GFQL's novel dataframe engine, and the GPU mode further adds single-GPU acceleration. Both the chain() and hop() methods are examined.\n",
+        "\n",
+        "* The benchmark does not examine bigger-than-memory and distributed scenarios. The provided results here are from running on a free Google Colab T4 runtime, with a 2.2GHz Intel CPU (12 GB CPU RAM) and T4 Nvidia GPU (16 GB GPU RAM)."
+      ],
+      "metadata": {
+        "id": "Sm80AgJOJ3-c"
+      }
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "## Install, Import, Load"
+      ],
+      "metadata": {
+        "id": "g7s-qBKqE9eC"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "# !pip install --extra-index-url=https://pypi.nvidia.com cuml-cu12 cudf-cu12\n",
+        "import cudf\n",
+        "cudf.__version__\n",
+        "\n",
+        "!pip install -q igraph\n",
+        "!pip install -q graphistry\n",
+        "\n",
+        "import pandas as pd\n",
+        "import graphistry, time, cProfile\n",
+        "\n",
+        "from graphistry import (\n",
+        "\n",
+        "    # graph operators\n",
+        "    n, e_undirected, e_forward, e_reverse,\n",
+        "\n",
+        "    # attribute predicates\n",
+        "    is_in, ge, startswith, contains, match as match_re\n",
+        ")\n",
+        "graphistry.__version__"
+      ],
+      "metadata": {
+        "id": "JTdSJgquBnGd",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 35
+        },
+        "outputId": "4d1da186-28ab-4236-a569-4dd8760c4715"
+      },
+      "execution_count": 5,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "'0.33.0'"
+            ],
+            "application/vnd.google.colaboratory.intrinsic+json": {
+              "type": "string"
+            }
+          },
+          "metadata": {},
+          "execution_count": 5
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 2,
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "yLJjLYAWbRXH",
+        "outputId": "e0177c6d-7d74-449a-c72b-28241516aaf0"
+      },
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "(81306, 1)"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 2
+        }
+      ],
+      "source": [
+        "te_df = pd.read_csv('https://snap.stanford.edu/data/twitter_combined.txt.gz', sep=' ', names=['s', 'd'])\n",
+        "g = graphistry.edges(te_df, 's', 'd').materialize_nodes()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "## .chain() CPU v GPU"
+      ],
+      "metadata": {
+        "id": "c3vuo0yVFDCs"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "start = time.time()\n",
+        "\n",
+        "for i in range(10):\n",
+        "  g2 = g.chain([n({'id': 17116707}), e_forward(hops=1)])\n",
+        "g2._nodes.shape, g2._edges.shape\n",
+        "\n",
+        "end1 = time.time()\n",
+        "T1 = end1 - start"
+      ],
+      "metadata": {
+        "id": "wEzyOOymCcsj"
+      },
+      "execution_count": null,
+      "outputs": []
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "start = time.time()\n",
+        "\n",
+        "g_gdf = g.nodes(lambda g: cudf.DataFrame(g._nodes)).edges(lambda g: cudf.DataFrame(g._edges))\n",
+        "for i in range(10):\n",
+        "  out = g_gdf.chain([n({'id': 17116707}), e_forward(hops=1)])._nodes\n",
+        "del g_gdf\n",
+        "del out\n",
+        "\n",
+        "end2 = time.time()\n",
+        "T2= end2 - start\n",
+        "print('CPU time:',T1, '\\nGPU time:', T2, '\\nspeedup:', T1/T2)"
+      ],
+      "metadata": {
+        "id": "yKoNh5UgClIr",
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "outputId": "5c9545e1-5a6c-45db-b0ab-a199939e8ebd"
+      },
+      "execution_count": 17,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "CPU time: 17.837570190429688 \n",
+            "GPU time: 2.0647764205932617 \n",
+            "speedup: 8.638983868919091\n"
+          ]
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "## .hop() CPU v GPU\n",
+        "\n",
+        "*   simpler tasks can witness greater speedup\n",
+        "\n"
+      ],
+      "metadata": {
+        "id": "KrXZ7ajHFJ3z"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "start = time.time()\n",
+        "start_nodes = pd.DataFrame({g._node: [17116707]})\n",
+        "for i in range(10):\n",
+        "  g2 = g.hop(\n",
+        "      nodes=start_nodes,\n",
+        "      direction='forward',\n",
+        "      hops=8)\n",
+        "\n",
+        "end1 = time.time()\n",
+        "T1 = end1 - start"
+      ],
+      "metadata": {
+        "id": "CJt_8YTPCtZM"
+      },
+      "execution_count": null,
+      "outputs": []
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "start = time.time()\n",
+        "start_nodes = cudf.DataFrame({g._node: [17116707]})\n",
+        "g_gdf = g.nodes(cudf.from_pandas(g._nodes)).edges(cudf.from_pandas(g._edges))\n",
+        "for i in range(10):\n",
+        "  g2 = g_gdf.hop(\n",
+        "      nodes=start_nodes,\n",
+        "      direction='forward',\n",
+        "      engine = 'cudf',  # one can also set `engine = cudf`\n",
+        "      hops=8)\n",
+        "del start_nodes\n",
+        "del g_gdf\n",
+        "del g2\n",
+        "\n",
+        "end2 = time.time()\n",
+        "T2= end2 - start\n",
+        "print('CPU time:',T1, '\\nGPU time:', T2, '\\nspeedup:', T1/T2)"
+      ],
+      "metadata": {
+        "id": "fOC7ODIeFTI6",
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "outputId": "ba349462-caee-4f42-8f45-fa7c883c54bc"
+      },
+      "execution_count": 26,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "CPU time: 40.91506862640381 \n",
+            "GPU time: 2.8351004123687744 \n",
+            "speedup: 14.431611821543413\n"
+          ]
+        }
+      ]
+    }
+  ]
+}
\ No newline at end of file

From ae4524237210121040ca1d583113f1a6f123a070 Mon Sep 17 00:00:00 2001
From: Daniel <dcolinmorgan@gmail.com>
Date: Tue, 9 Jul 2024 16:11:46 +0200
Subject: [PATCH 2/5] revise initial notebook, print df, loop hops

---
 demos/gfql/benchmark_hops_cpu_gpu.ipynb | 5899 ++++++++++-------------
 demos/gfql/gfql_cpv_gpu_enchmark.ipynb  | 2976 ------------
 demos/gfql/simple_gfql_notebook.ipynb   |  264 -
 3 files changed, 2535 insertions(+), 6604 deletions(-)
 delete mode 100644 demos/gfql/gfql_cpv_gpu_enchmark.ipynb
 delete mode 100644 demos/gfql/simple_gfql_notebook.ipynb

diff --git a/demos/gfql/benchmark_hops_cpu_gpu.ipynb b/demos/gfql/benchmark_hops_cpu_gpu.ipynb
index bf17b630e7..869344af4c 100644
--- a/demos/gfql/benchmark_hops_cpu_gpu.ipynb
+++ b/demos/gfql/benchmark_hops_cpu_gpu.ipynb
@@ -1,27 +1,14 @@
 {
-  "nbformat": 4,
-  "nbformat_minor": 0,
-  "metadata": {
-    "colab": {
-      "provenance": [],
-      "gpuType": "T4"
-    },
-    "kernelspec": {
-      "name": "python3",
-      "display_name": "Python 3"
-    },
-    "language_info": {
-      "name": "python"
-    },
-    "accelerator": "GPU"
-  },
   "cells": [
     {
       "cell_type": "markdown",
+      "metadata": {
+        "id": "GZxoiU8sQDk_"
+      },
       "source": [
         "# GFQL CPU, GPU Benchmark\n",
         "\n",
-        "This notebook examines GFQL progerty graph query performance on 1-8 hop queries using CPU + GPU modes on various real-world 100K - 100M edge graphs. The data comes from a variety of popular social networks. The single-threaded CPU mode benefits from GFQL's novel dataframe engine, and the GPU mode further adds single-GPU acceleration. Both the `chain()` and `hop()` methods are examined.\n",
+        "This notebook examines GFQL property graph query performance on 1-8 hop queries using CPU + GPU modes on various real-world 100K - 100M edge graphs. The data comes from a variety of popular social networks. The single-threaded CPU mode benefits from GFQL's novel dataframe engine, and the GPU mode further adds single-GPU acceleration. Both the `chain()` and `hop()` methods are examined.\n",
         "\n",
         "The benchmark does not examine bigger-than-memory and distributed scenarios. The provided results here are from running on a free Google Colab T4 runtime, with a 2.2GHz Intel CPU (12 GB CPU RAM) and T4 Nvidia GPU (16 GB GPU RAM).\n",
         "\n",
@@ -30,10 +17,10 @@
         "\n",
         "| Network | Nodes     | Edges        |\n",
         "|-------------|-----------|--------------|\n",
-        "| **Facebook**| 4,039     | 88,234       |\n",
-        "| **Twitter** | 81,306    | 2,420,766    |\n",
-        "| **GPlus**   | 107,614   | 30,494,866   |\n",
-        "| **Orkut**   | 3,072,441 | 117,185,082  |\n",
+        "| [**Facebook**](#fb)| 4,039     | 88,234       |\n",
+        "| [**Twitter**](#tw) | 81,306    | 2,420,766    |\n",
+        "| [**GPlus**](#gpl)   | 107,614   | 30,494,866   |\n",
+        "| [**Orkut**](#ork)   | 3,072,441 | 117,185,082  |\n",
         "\n",
         "## Results\n",
         "\n",
@@ -52,10 +39,10 @@
         "\n",
         "| **Dataset** | Max GPU Speedup      | CPU GTEPS   | GPU GTEPS   | T CPU edges / \\$ (t3.l) | T GPU edges / \\$ (g4dn.xl) |\n",
         "|-------------|--------------|-------------|-------------|----------------------------|--------------------------------|\n",
-        "| **Facebook**| 1.1X  | 0.66 | 0.61 | 65.7                | 10.4                    |\n",
-        "| **Twitter** | 17.4X   | 0.17 | 2.81 | 16.7                | 48.1                    |\n",
-        "| **GPlus**   | 43.8X  | 0.09 | 2.87 | 8.5                | 49.2                    |\n",
-        "| **Orkut**   | N/A            | N/A         | 12.15 | N/A                        | 208.3                    |\n",
+        "| [**Facebook**](#fb)| 1.1X  | 0.66 | 0.61 | 65.7                | 10.4                    |\n",
+        "| [**Twitter**](#tw) | 17.4X   | 0.17 | 2.81 | 16.7                | 48.1                    |\n",
+        "| [**GPlus**](#gpl)   | 43.8X  | 0.09 | 2.87 | 8.5                | 49.2                    |\n",
+        "| [**Orkut**](#ork)   | N/A            | N/A         | 12.15 | N/A                        | 208.3                    |\n",
         "| **AVG** | 20.7X | 0.30 | 4.61 | 30.3 | 79.0\n",
         "| **MAX** | 43.8X | 0.66 | 12.15 | 65.7 | 208.3\n",
         "\n",
@@ -67,53 +54,46 @@
         "\n",
         "| **Dataset** | Max GPU Speedup | CPU GTEPS | GPU GTEPS | T CPU edges / \\$ (t3.l) | T GPU edges / \\$ (g4dn.xl) |\n",
         "|-------------|-------------|-----------|-----------|--------------------|--------------------------------|\n",
-        "| **Facebook**| 3X          | 0.47      | 1.47     | 47.0        | 25.2                    |\n",
-        "| **Twitter** | 42X         | 0.50      | 10.51      | 50.2        | 180.2                    |\n",
-        "| **GPlus**   | 21X         | 0.26      | 4.11       | 26.2        | 70.4                    |\n",
-        "| **Orkut**   | N/A         | N/A       | 41.50     | N/A                | 711.4                    |\n",
+        "| [**Facebook**](#fb)| 3X          | 0.47      | 1.47     | 47.0        | 25.2                    |\n",
+        "| [**Twitter**](#tw) | 42X         | 0.50      | 10.51      | 50.2        | 180.2                    |\n",
+        "| [**GPlus**](#gpl)   | 21X         | 0.26      | 4.11       | 26.2        | 70.4                    |\n",
+        "| [**Orkut**](#ork)   | N/A         | N/A       | 41.50     | N/A                | 711.4                    |\n",
         "| **AVG** | 22X | 0.41 | 14.4 | 41.1 | 246.8\n",
         "| **MAX** | 42X | 0.50 | 41.50 | 50.2 | 711.4\n"
-      ],
-      "metadata": {
-        "id": "GZxoiU8sQDk_"
-      }
+      ]
     },
     {
       "cell_type": "markdown",
-      "source": [
-        "## Optional: GPU setup - Google Colab"
-      ],
       "metadata": {
         "id": "SAj8lhREEOwS"
-      }
+      },
+      "source": [
+        "## Optional: GPU setup - Google Colab"
+      ]
     },
     {
       "cell_type": "markdown",
-      "source": [],
       "metadata": {
         "id": "4hrEEAAm7DTO"
-      }
+      },
+      "source": []
     },
     {
       "cell_type": "code",
-      "source": [
-        "# Report GPU used when GPU benchmarking\n",
-        "! nvidia-smi"
-      ],
+      "execution_count": 1,
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/"
         },
         "id": "W2MF6ZsjDv3B",
-        "outputId": "46088cbc-2db9-4529-f724-dc57ed85dfb7"
+        "outputId": "ad2ab798-617d-49db-e379-5670debe4951"
       },
-      "execution_count": 1,
       "outputs": [
         {
           "output_type": "stream",
           "name": "stdout",
           "text": [
-            "Tue Dec 26 00:50:30 2023       \n",
+            "Tue Jul  9 13:29:05 2024       \n",
             "+---------------------------------------------------------------------------------------+\n",
             "| NVIDIA-SMI 535.104.05             Driver Version: 535.104.05   CUDA Version: 12.2     |\n",
             "|-----------------------------------------+----------------------+----------------------+\n",
@@ -122,7 +102,7 @@
             "|                                         |                      |               MIG M. |\n",
             "|=========================================+======================+======================|\n",
             "|   0  Tesla T4                       Off | 00000000:00:04.0 Off |                    0 |\n",
-            "| N/A   54C    P8              10W /  70W |      0MiB / 15360MiB |      0%      Default |\n",
+            "| N/A   41C    P8              10W /  70W |      0MiB / 15360MiB |      0%      Default |\n",
             "|                                         |                      |                  N/A |\n",
             "+-----------------------------------------+----------------------+----------------------+\n",
             "                                                                                         \n",
@@ -135,198 +115,176 @@
             "+---------------------------------------------------------------------------------------+\n"
           ]
         }
-      ]
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "# if in google colab\n",
-        "!git clone https://github.com/rapidsai/rapidsai-csp-utils.git\n",
-        "!python rapidsai-csp-utils/colab/pip-install.py"
       ],
-      "metadata": {
-        "id": "Aikh0x4ID_wK"
-      },
-      "execution_count": 8,
-      "outputs": []
+      "source": [
+        "# Report GPU used when GPU benchmarking\n",
+        "! nvidia-smi"
+      ]
     },
     {
       "cell_type": "code",
-      "source": [
-        "import cudf\n",
-        "cudf.__version__"
-      ],
+      "execution_count": 2,
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/",
           "height": 35
         },
         "id": "Lwekdei1dH3N",
-        "outputId": "71f5b01d-7917-4283-8338-969167d6e1e8"
+        "outputId": "51562461-432e-4b8d-f697-0a6b559ac8b0"
       },
-      "execution_count": 3,
       "outputs": [
         {
           "output_type": "execute_result",
           "data": {
             "text/plain": [
-              "'23.12.01'"
+              "'24.04.01'"
             ],
             "application/vnd.google.colaboratory.intrinsic+json": {
               "type": "string"
             }
           },
           "metadata": {},
-          "execution_count": 3
+          "execution_count": 2
         }
+      ],
+      "source": [
+        "import cudf\n",
+        "cudf.__version__"
       ]
     },
     {
       "cell_type": "markdown",
-      "source": [
-        "# 1. Install & configure"
-      ],
       "metadata": {
         "id": "QQpsrtwBT7sa"
-      }
+      },
+      "source": [
+        "# 1. Install & configure"
+      ]
     },
     {
       "cell_type": "code",
-      "source": [
-        "#! pip install graphistry[igraph]\n",
-        "\n",
-        "!pip install -q igraph\n",
-        "#!pip install -q git+https://github.com/graphistry/pygraphistry.git@dev/cugfql\n",
-        "!pip install -q graphistry\n"
-      ],
+      "execution_count": 3,
       "metadata": {
-        "id": "cYjRbgkU9Sx8",
         "colab": {
           "base_uri": "https://localhost:8080/"
         },
-        "outputId": "2cf25531-9b8b-4715-ccc7-e79094d84ebd"
+        "id": "cYjRbgkU9Sx8",
+        "outputId": "c8e454a2-e537-467e-afc6-830c51ad869c"
       },
-      "execution_count": 2,
       "outputs": [
         {
           "output_type": "stream",
           "name": "stdout",
           "text": [
-            "  Preparing metadata (setup.py) ... \u001b[?25l\u001b[?25hdone\n"
+            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m3.1/3.1 MB\u001b[0m \u001b[31m13.1 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
+            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m250.5/250.5 kB\u001b[0m \u001b[31m4.7 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
+            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m332.3/332.3 kB\u001b[0m \u001b[31m9.0 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
+            "\u001b[?25h"
           ]
         }
+      ],
+      "source": [
+        "#! pip install graphistry[igraph]\n",
+        "\n",
+        "!pip install -q igraph\n",
+        "!pip install -q graphistry\n"
       ]
     },
     {
       "cell_type": "markdown",
-      "source": [
-        "## Imports"
-      ],
       "metadata": {
         "id": "Ff6Tt9DhkePl"
-      }
+      },
+      "source": [
+        "## Imports"
+      ]
     },
     {
       "cell_type": "code",
-      "source": [
-        "import pandas as pd\n",
-        "\n",
-        "import graphistry\n",
-        "\n",
-        "from graphistry import (\n",
-        "\n",
-        "    # graph operators\n",
-        "    n, e_undirected, e_forward, e_reverse,\n",
-        "\n",
-        "    # attribute predicates\n",
-        "    is_in, ge, startswith, contains, match as match_re\n",
-        ")\n",
-        "graphistry.__version__"
-      ],
+      "execution_count": 4,
       "metadata": {
-        "id": "S5_y0CbLkjft",
         "colab": {
           "base_uri": "https://localhost:8080/",
           "height": 35
         },
-        "outputId": "a68a9c4b-c9c5-4b8b-ea4f-7bf1e4ddf315"
+        "id": "S5_y0CbLkjft",
+        "outputId": "c8afe192-51c8-45d2-a79e-c1902200e6a3"
       },
-      "execution_count": 3,
       "outputs": [
         {
           "output_type": "execute_result",
           "data": {
             "text/plain": [
-              "'0.32.0+12.g72e778c'"
+              "'0.33.9'"
             ],
             "application/vnd.google.colaboratory.intrinsic+json": {
               "type": "string"
             }
           },
           "metadata": {},
-          "execution_count": 3
+          "execution_count": 4
         }
+      ],
+      "source": [
+        "import pandas as pd\n",
+        "import numpy as np\n",
+        "import graphistry, time\n",
+        "\n",
+        "from graphistry import (\n",
+        "\n",
+        "    # graph operators\n",
+        "    n, e_undirected, e_forward, e_reverse,\n",
+        "\n",
+        "    # attribute predicates\n",
+        "    is_in, ge, startswith, contains, match as match_re\n",
+        ")\n",
+        "graphistry.__version__"
       ]
     },
     {
       "cell_type": "code",
-      "source": [
-        "import cudf"
-      ],
+      "execution_count": 5,
       "metadata": {
-        "id": "I7Fg75jsG4co"
+        "id": "uLZKph2-a5M4"
       },
-      "execution_count": 6,
-      "outputs": []
-    },
-    {
-      "cell_type": "code",
+      "outputs": [],
       "source": [
         "#work around google colab shell encoding bugs\n",
         "\n",
         "import locale\n",
         "locale.getpreferredencoding = lambda: \"UTF-8\""
-      ],
-      "metadata": {
-        "id": "uLZKph2-a5M4"
-      },
-      "execution_count": 7,
-      "outputs": []
+      ]
     },
     {
       "cell_type": "markdown",
-      "source": [
-        "# 2. Perf benchmarks"
-      ],
       "metadata": {
         "id": "eU9SyauNUHtR"
-      }
+      },
+      "source": [
+        "# 2. Perf benchmarks"
+      ]
     },
     {
       "cell_type": "markdown",
-      "source": [
-        "### Facebook: 88K edges"
-      ],
       "metadata": {
         "id": "NA0Ym11fkB8j"
-      }
+      },
+      "source": [
+        "<a name=\"fb\"></a>\n",
+        "### Facebook: 88K edges"
+      ]
     },
     {
       "cell_type": "code",
-      "source": [
-        "df = pd.read_csv('https://raw.githubusercontent.com/graphistry/pygraphistry/master/demos/data/facebook_combined.txt', sep=' ', names=['s', 'd'])\n",
-        "print(df.shape)\n",
-        "df.head(5)"
-      ],
+      "execution_count": 6,
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/",
           "height": 224
         },
         "id": "vXuQogHekClJ",
-        "outputId": "64db92c0-2704-438b-d0e4-25865acbb5e9"
+        "outputId": "e984cfbd-ad39-4902-918d-598f342e6f06"
       },
-      "execution_count": 10,
       "outputs": [
         {
           "output_type": "stream",
@@ -348,7 +306,7 @@
             ],
             "text/html": [
               "\n",
-              "  <div id=\"df-1ff270ef-f23b-4ff0-aff0-61786d9d4eeb\" class=\"colab-df-container\">\n",
+              "  <div id=\"df-b4a8ec43-cae0-4d9f-9c46-33f37d3d4a4a\" class=\"colab-df-container\">\n",
               "    <div>\n",
               "<style scoped>\n",
               "    .dataframe tbody tr th:only-of-type {\n",
@@ -403,7 +361,7 @@
               "    <div class=\"colab-df-buttons\">\n",
               "\n",
               "  <div class=\"colab-df-container\">\n",
-              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-1ff270ef-f23b-4ff0-aff0-61786d9d4eeb')\"\n",
+              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-b4a8ec43-cae0-4d9f-9c46-33f37d3d4a4a')\"\n",
               "            title=\"Convert this dataframe to an interactive table.\"\n",
               "            style=\"display:none;\">\n",
               "\n",
@@ -455,12 +413,12 @@
               "\n",
               "    <script>\n",
               "      const buttonEl =\n",
-              "        document.querySelector('#df-1ff270ef-f23b-4ff0-aff0-61786d9d4eeb button.colab-df-convert');\n",
+              "        document.querySelector('#df-b4a8ec43-cae0-4d9f-9c46-33f37d3d4a4a button.colab-df-convert');\n",
               "      buttonEl.style.display =\n",
               "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
               "\n",
               "      async function convertToInteractive(key) {\n",
-              "        const element = document.querySelector('#df-1ff270ef-f23b-4ff0-aff0-61786d9d4eeb');\n",
+              "        const element = document.querySelector('#df-b4a8ec43-cae0-4d9f-9c46-33f37d3d4a4a');\n",
               "        const dataTable =\n",
               "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
               "                                                    [key], {});\n",
@@ -480,8 +438,8 @@
               "  </div>\n",
               "\n",
               "\n",
-              "<div id=\"df-54260500-6469-4e75-a1c8-1241a1fc89a1\">\n",
-              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-54260500-6469-4e75-a1c8-1241a1fc89a1')\"\n",
+              "<div id=\"df-5aa819dc-d8d4-4a1e-bd27-fbc9525225d9\">\n",
+              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-5aa819dc-d8d4-4a1e-bd27-fbc9525225d9')\"\n",
               "            title=\"Suggest charts\"\n",
               "            style=\"display:none;\">\n",
               "\n",
@@ -600,37 +558,43 @@
               "    }\n",
               "    (() => {\n",
               "      let quickchartButtonEl =\n",
-              "        document.querySelector('#df-54260500-6469-4e75-a1c8-1241a1fc89a1 button');\n",
+              "        document.querySelector('#df-5aa819dc-d8d4-4a1e-bd27-fbc9525225d9 button');\n",
               "      quickchartButtonEl.style.display =\n",
               "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
               "    })();\n",
               "  </script>\n",
               "</div>\n",
+              "\n",
               "    </div>\n",
               "  </div>\n"
-            ]
+            ],
+            "application/vnd.google.colaboratory.intrinsic+json": {
+              "type": "dataframe",
+              "variable_name": "df",
+              "summary": "{\n  \"name\": \"df\",\n  \"rows\": 88234,\n  \"fields\": [\n    {\n      \"column\": \"s\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 910,\n        \"min\": 0,\n        \"max\": 4031,\n        \"num_unique_values\": 3663,\n        \"samples\": [\n          1624,\n          101,\n          377\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"d\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 893,\n        \"min\": 1,\n        \"max\": 4038,\n        \"num_unique_values\": 4037,\n        \"samples\": [\n          2193,\n          150,\n          879\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
+            }
           },
           "metadata": {},
-          "execution_count": 10
+          "execution_count": 6
         }
+      ],
+      "source": [
+        "df = pd.read_csv('https://raw.githubusercontent.com/graphistry/pygraphistry/master/demos/data/facebook_combined.txt', sep=' ', names=['s', 'd'])\n",
+        "print(df.shape)\n",
+        "df.head(5)"
       ]
     },
     {
       "cell_type": "code",
-      "source": [
-        "fg = graphistry.edges(df, 's', 'd').materialize_nodes()\n",
-        "print(fg._nodes.shape, fg._edges.shape)\n",
-        "fg._nodes.head(5)"
-      ],
+      "execution_count": 8,
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/",
           "height": 224
         },
         "id": "jEma7hvvkzkN",
-        "outputId": "dbf21342-6b80-429c-bd3f-b1494c6854c7"
+        "outputId": "b017dccd-c859-4bbf-e417-a8a3d268d002"
       },
-      "execution_count": 11,
       "outputs": [
         {
           "output_type": "stream",
@@ -652,7 +616,7 @@
             ],
             "text/html": [
               "\n",
-              "  <div id=\"df-6855e11a-489c-4631-b518-effafab7d91f\" class=\"colab-df-container\">\n",
+              "  <div id=\"df-3b3a72e7-5795-45f5-887d-c0fcb534b2fe\" class=\"colab-df-container\">\n",
               "    <div>\n",
               "<style scoped>\n",
               "    .dataframe tbody tr th:only-of-type {\n",
@@ -701,7 +665,7 @@
               "    <div class=\"colab-df-buttons\">\n",
               "\n",
               "  <div class=\"colab-df-container\">\n",
-              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-6855e11a-489c-4631-b518-effafab7d91f')\"\n",
+              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-3b3a72e7-5795-45f5-887d-c0fcb534b2fe')\"\n",
               "            title=\"Convert this dataframe to an interactive table.\"\n",
               "            style=\"display:none;\">\n",
               "\n",
@@ -753,12 +717,12 @@
               "\n",
               "    <script>\n",
               "      const buttonEl =\n",
-              "        document.querySelector('#df-6855e11a-489c-4631-b518-effafab7d91f button.colab-df-convert');\n",
+              "        document.querySelector('#df-3b3a72e7-5795-45f5-887d-c0fcb534b2fe button.colab-df-convert');\n",
               "      buttonEl.style.display =\n",
               "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
               "\n",
               "      async function convertToInteractive(key) {\n",
-              "        const element = document.querySelector('#df-6855e11a-489c-4631-b518-effafab7d91f');\n",
+              "        const element = document.querySelector('#df-3b3a72e7-5795-45f5-887d-c0fcb534b2fe');\n",
               "        const dataTable =\n",
               "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
               "                                                    [key], {});\n",
@@ -778,8 +742,8 @@
               "  </div>\n",
               "\n",
               "\n",
-              "<div id=\"df-e67d6c07-7215-434e-a899-7b42d2724764\">\n",
-              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-e67d6c07-7215-434e-a899-7b42d2724764')\"\n",
+              "<div id=\"df-41edf1d7-e1a7-4504-a262-474f20883abe\">\n",
+              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-41edf1d7-e1a7-4504-a262-474f20883abe')\"\n",
               "            title=\"Suggest charts\"\n",
               "            style=\"display:none;\">\n",
               "\n",
@@ -898,1301 +862,122 @@
               "    }\n",
               "    (() => {\n",
               "      let quickchartButtonEl =\n",
-              "        document.querySelector('#df-e67d6c07-7215-434e-a899-7b42d2724764 button');\n",
+              "        document.querySelector('#df-41edf1d7-e1a7-4504-a262-474f20883abe button');\n",
               "      quickchartButtonEl.style.display =\n",
               "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
               "    })();\n",
               "  </script>\n",
               "</div>\n",
+              "\n",
               "    </div>\n",
               "  </div>\n"
-            ]
+            ],
+            "application/vnd.google.colaboratory.intrinsic+json": {
+              "type": "dataframe",
+              "summary": "{\n  \"name\": \"fg\",\n  \"rows\": 5,\n  \"fields\": [\n    {\n      \"column\": \"id\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 1,\n        \"min\": 0,\n        \"max\": 4,\n        \"num_unique_values\": 5,\n        \"samples\": [\n          1,\n          4,\n          2\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
+            }
           },
           "metadata": {},
-          "execution_count": 11
+          "execution_count": 8
         }
-      ]
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "for i in range(100):\n",
-        "  fg2 = fg.chain([n({'id': 0}), e_forward(hops=2)])"
       ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "5lEdCBw9lzd7",
-        "outputId": "ed7451e0-401e-4edc-c8de-79c5afd0c95b"
-      },
-      "execution_count": 12,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "CPU times: user 13.6 s, sys: 2.08 s, total: 15.7 s\n",
-            "Wall time: 18 s\n"
-          ]
-        }
+      "source": [
+        "fg = graphistry.edges(df, 's', 'd').materialize_nodes()\n",
+        "print(fg._nodes.shape, fg._edges.shape)\n",
+        "fg._nodes.head(5)"
       ]
     },
     {
-      "cell_type": "code",
+      "cell_type": "markdown",
       "source": [
-        "%%time\n",
-        "fg_gdf = fg.nodes(lambda g: cudf.DataFrame(g._nodes)).edges(lambda g: cudf.DataFrame(g._edges))\n",
-        "for i in range(100):\n",
-        "  fg2 = fg_gdf.chain([n({'id': 0}), e_forward(hops=2)])\n",
-        "print(fg._nodes.shape, fg._edges.shape)\n",
-        "print(fg2._nodes.shape, fg2._edges.shape)\n",
-        "del fg_gdf\n",
-        "del fg2"
+        "with 2 and 5 hop `chain` comparison we see a slight/negligable speedup enabled by setting g. to `cudf`"
       ],
       "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "JFKIBa8mJCvJ",
-        "outputId": "c22022f0-b33d-483a-db64-29992c5161e8"
-      },
-      "execution_count": null,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "(4039, 1) (88234, 2)\n",
-            "(1519, 1) (4060, 2)\n",
-            "CPU times: user 11.8 s, sys: 28.1 ms, total: 11.8 s\n",
-            "Wall time: 11.9 s\n"
-          ]
-        }
-      ]
+        "id": "2gVDho9cn2Et"
+      }
     },
     {
       "cell_type": "code",
       "source": [
-        "%%time\n",
-        "for i in range(50):\n",
-        "  fg2 = fg.chain([n({'id': 0}), e_forward(hops=5)])\n",
-        "print(fg._nodes.shape, fg._edges.shape)\n",
-        "print(fg2._nodes.shape, fg2._edges.shape)"
+        "results_df = pd.DataFrame(columns=['hops', 'CPU n_notation time (s)', 'GPU n_notation time (s)', 'n_notation speedup',\n",
+        "                                   'CPU source_node_match time (s)', 'GPU source_node_match time (s)', 'source_node_match speedup'])\n",
+        "\n",
+        "\n",
+        "for n_hop in [2,5]:\n",
+        "    start0 = time.time()\n",
+        "    for i in range(100):\n",
+        "        fg2 = fg.chain([n({'id': 0}), e_forward(hops=n_hop)])  # using n notation\n",
+        "    mid0 = time.time()\n",
+        "    for i in range(100):\n",
+        "        fg2 = fg.chain([e_forward(source_node_match={'id': 0}, hops=n_hop)])  # using source_node_match in e_forward\n",
+        "    end0 = time.time()\n",
+        "    T0 = mid0-start0\n",
+        "    T1 = end0-mid0\n",
+        "    fg_gdf = fg.nodes(lambda g: cudf.DataFrame(g._nodes)).edges(lambda g: cudf.DataFrame(g._edges))\n",
+        "    start1 = time.time()\n",
+        "    for i in range(100):\n",
+        "        fg2 = fg_gdf.chain([n({'id': 0}), e_forward(hops=n_hop)])\n",
+        "    mid1 = time.time()\n",
+        "    for i in range(100):\n",
+        "        fg2 = fg_gdf.chain([e_forward(source_node_match={'id': 0}, hops=n_hop)])\n",
+        "    end1 = time.time()\n",
+        "\n",
+        "    del fg_gdf\n",
+        "    del fg2\n",
+        "    T2 = mid1-start1\n",
+        "    T3 = end1-mid1\n",
+        "\n",
+        "    new_row = pd.DataFrame({\n",
+        "        'hops': [n_hop],\n",
+        "        'CPU n_notation time (s)': [np.round(T0, 4)],\n",
+        "        'GPU n_notation time (s)': [np.round(T2, 4)],\n",
+        "        'n_notation speedup': [np.round(T0 / T2, 4)],\n",
+        "        'CPU source_node_match time (s)': [np.round(T1, 4)],\n",
+        "        'GPU source_node_match time (s)': [np.round(T3, 4)],\n",
+        "        'source_node_match speedup': [np.round(T1 / T3, 4)],\n",
+        "    })\n",
+        "\n",
+        "    results_df = pd.concat([results_df, new_row], ignore_index=True)\n",
+        "\n",
+        "(results_df)"
       ],
       "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "-KBGLexek5tS",
-        "outputId": "2f462e6c-578a-4fa1-ec29-91bae753f4c5"
+        "id": "ZKzoqGcdxekr"
       },
       "execution_count": null,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "(4039, 1) (88234, 2)\n",
-            "(3829, 1) (86074, 2)\n",
-            "CPU times: user 15.4 s, sys: 808 ms, total: 16.2 s\n",
-            "Wall time: 16.2 s\n"
-          ]
-        }
-      ]
+      "outputs": []
     },
     {
       "cell_type": "code",
       "source": [
-        "%%time\n",
-        "fg_gdf = fg.nodes(lambda g: cudf.DataFrame(g._nodes)).edges(lambda g: cudf.DataFrame(g._edges))\n",
-        "for i in range(50):\n",
-        "  fg2 = fg_gdf.chain([n({'id': 0}), e_forward(hops=5)])\n",
-        "print(fg._nodes.shape, fg._edges.shape)\n",
-        "print(fg2._nodes.shape, fg2._edges.shape)\n",
-        "del fg_gdf\n",
-        "del fg2"
+        "results_df.T"
       ],
       "metadata": {
         "colab": {
-          "base_uri": "https://localhost:8080/"
+          "base_uri": "https://localhost:8080/",
+          "height": 269
         },
-        "id": "CVpcbhpdHFEF",
-        "outputId": "aba04ee1-781e-4226-b593-b42415a55fc4"
+        "id": "W8BK9GnjtGlN",
+        "outputId": "55a88806-1151-47c1-c10d-457b5193b3cf"
       },
-      "execution_count": null,
+      "execution_count": 10,
       "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "(4039, 1) (88234, 2)\n",
-            "(3829, 1) (86074, 2)\n",
-            "CPU times: user 9.82 s, sys: 133 ms, total: 9.95 s\n",
-            "Wall time: 10.1 s\n"
-          ]
-        }
-      ]
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "for i in range(100):\n",
-        "  fg2 = fg.chain([e_forward(source_node_match={'id': 0}, hops=5)])"
-      ],
-      "metadata": {
-        "id": "1cFIyJF9pLjE",
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "outputId": "107329af-8e4b-428c-8b03-77ed00bdf5bf"
-      },
-      "execution_count": null,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "CPU times: user 11.8 s, sys: 377 ms, total: 12.1 s\n",
-            "Wall time: 13.1 s\n"
-          ]
-        }
-      ]
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "fg_gdf = fg.nodes(lambda g: cudf.DataFrame(g._nodes)).edges(lambda g: cudf.DataFrame(g._edges))\n",
-        "for i in range(100):\n",
-        "  fg2 = fg_gdf.chain([e_forward(source_node_match={'id': 0}, hops=5)])\n",
-        "print(fg._nodes.shape, fg._edges.shape)\n",
-        "print(fg2._nodes.shape, fg2._edges.shape)\n",
-        "del fg_gdf\n",
-        "del fg2\n",
-        "\n"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "M5uRiD6uJVNW",
-        "outputId": "5e938a19-2992-4280-80c2-784382d40113"
-      },
-      "execution_count": null,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "(4039, 1) (88234, 2)\n",
-            "(348, 1) (347, 2)\n",
-            "CPU times: user 14.1 s, sys: 48.5 ms, total: 14.2 s\n",
-            "Wall time: 14.2 s\n"
-          ]
-        }
-      ]
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "start_nodes = pd.DataFrame({fg._node: [0]})\n",
-        "for i in range(100):\n",
-        "  fg2 = fg.hop(\n",
-        "      nodes=start_nodes,\n",
-        "      direction='forward',\n",
-        "      hops=2)\n",
-        "print(fg2._nodes.shape, fg2._edges.shape)"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "Y9vgzfT69x41",
-        "outputId": "6882c1ce-0df8-4087-dda4-0a105a8617e1"
-      },
-      "execution_count": 17,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "(1519, 1) (4060, 2)\n",
-            "CPU times: user 4.5 s, sys: 1.35 s, total: 5.85 s\n",
-            "Wall time: 6.09 s\n"
-          ]
-        }
-      ]
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "start_nodes = cudf.DataFrame({fg._node: [0]})\n",
-        "fg_gdf = fg.nodes(cudf.from_pandas(fg._nodes)).edges(cudf.from_pandas(fg._edges))\n",
-        "for i in range(100):\n",
-        "  fg2 = fg_gdf.hop(\n",
-        "      nodes=start_nodes,\n",
-        "      direction='forward',\n",
-        "      hops=2)\n",
-        "print(fg2._nodes.shape, fg2._edges.shape)\n",
-        "del start_nodes\n",
-        "del fg_gdf\n",
-        "del fg2"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "c7ybJqjc-T31",
-        "outputId": "37ccc1fb-6460-4193-8aa7-22837ff06d0a"
-      },
-      "execution_count": 18,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "(1519, 1) (4060, 2)\n",
-            "CPU times: user 2.58 s, sys: 6.75 ms, total: 2.59 s\n",
-            "Wall time: 2.58 s\n"
-          ]
-        }
-      ]
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "start_nodes = pd.DataFrame({fg._node: [0]})\n",
-        "for i in range(100):\n",
-        "  fg2 = fg.hop(\n",
-        "      nodes=start_nodes,\n",
-        "      direction='forward',\n",
-        "      hops=5)\n",
-        "print(fg2._nodes.shape, fg2._edges.shape)"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "Dy7a4zDZ-7_G",
-        "outputId": "077b5d9c-c9ae-411a-8228-3c026b07a910"
-      },
-      "execution_count": 19,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "(3829, 1) (86074, 2)\n",
-            "CPU times: user 13.2 s, sys: 2 s, total: 15.2 s\n",
-            "Wall time: 18.3 s\n"
-          ]
-        }
-      ]
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "start_nodes = cudf.DataFrame({fg._node: [0]})\n",
-        "fg_gdf = fg.nodes(cudf.from_pandas(fg._nodes)).edges(cudf.from_pandas(fg._edges))\n",
-        "for i in range(100):\n",
-        "  fg2 = fg_gdf.hop(\n",
-        "      nodes=start_nodes,\n",
-        "      direction='forward',\n",
-        "      hops=5)\n",
-        "print(fg2._nodes.shape, fg2._edges.shape)\n",
-        "del start_nodes\n",
-        "del fg_gdf\n",
-        "del fg2"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "N5aUtF1a--ML",
-        "outputId": "0c2b67b8-fac6-45b3-dfbe-8002b5506e91"
-      },
-      "execution_count": 20,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "(3829, 1) (86074, 2)\n",
-            "CPU times: user 5.72 s, sys: 159 ms, total: 5.88 s\n",
-            "Wall time: 5.86 s\n"
-          ]
-        }
-      ]
-    },
-    {
-      "cell_type": "markdown",
-      "source": [
-        "## Twitter\n",
-        "\n",
-        "- edges: 2420766\n",
-        "- nodes: 81306"
-      ],
-      "metadata": {
-        "id": "KrJKjXy2KLos"
-      }
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "! wget 'https://snap.stanford.edu/data/twitter_combined.txt.gz'\n",
-        "#! curl -L 'https://snap.stanford.edu/data/twitter_combined.txt.gz' -o twitter_combined.txt.gz"
-      ],
-      "metadata": {
-        "id": "fO2qasGqpubr",
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "outputId": "d41a110e-9f7c-4710-9ce3-3f4906ab02ae"
-      },
-      "execution_count": 21,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "--2023-12-25 21:58:27--  https://snap.stanford.edu/data/twitter_combined.txt.gz\n",
-            "Resolving snap.stanford.edu (snap.stanford.edu)... 171.64.75.80\n",
-            "Connecting to snap.stanford.edu (snap.stanford.edu)|171.64.75.80|:443... connected.\n",
-            "HTTP request sent, awaiting response... 200 OK\n",
-            "Length: 10621918 (10M) [application/x-gzip]\n",
-            "Saving to: ‘twitter_combined.txt.gz’\n",
-            "\n",
-            "twitter_combined.tx 100%[===================>]  10.13M  3.00MB/s    in 4.0s    \n",
-            "\n",
-            "2023-12-25 21:58:32 (2.52 MB/s) - ‘twitter_combined.txt.gz’ saved [10621918/10621918]\n",
-            "\n"
-          ]
-        }
-      ]
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "! gunzip twitter_combined.txt.gz"
-      ],
-      "metadata": {
-        "id": "fn7zeA3SGlEo"
-      },
-      "execution_count": 22,
-      "outputs": []
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "! head -n 5 twitter_combined.txt"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "68TAZkhLGz9g",
-        "outputId": "8ba7c23d-267f-4b59-d6c6-b3f66caec9cf"
-      },
-      "execution_count": 24,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "214328887 34428380\n",
-            "17116707 28465635\n",
-            "380580781 18996905\n",
-            "221036078 153460275\n",
-            "107830991 17868918\n"
-          ]
-        }
-      ]
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "te_df = pd.read_csv('twitter_combined.txt', sep=' ', names=['s', 'd'])\n",
-        "te_df.shape"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "QU2wNeGXG2GC",
-        "outputId": "349ac9c0-6f6c-4ce6-fec0-8bae75fca635"
-      },
-      "execution_count": 25,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "CPU times: user 474 ms, sys: 61.9 ms, total: 536 ms\n",
-            "Wall time: 534 ms\n"
-          ]
-        },
         {
           "output_type": "execute_result",
           "data": {
             "text/plain": [
-              "(2420766, 2)"
-            ]
-          },
-          "metadata": {},
-          "execution_count": 25
-        }
-      ]
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "import graphistry"
-      ],
-      "metadata": {
-        "id": "EK5gQH2iG5UU"
-      },
-      "execution_count": 26,
-      "outputs": []
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "g = graphistry.edges(te_df, 's', 'd').materialize_nodes()\n",
-        "g._nodes.shape"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "ZtIW-eFGG_R4",
-        "outputId": "0686e9b3-b684-4b93-da03-289244394338"
-      },
-      "execution_count": 27,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "CPU times: user 86.4 ms, sys: 106 ms, total: 193 ms\n",
-            "Wall time: 191 ms\n"
-          ]
-        },
-        {
-          "output_type": "execute_result",
-          "data": {
-            "text/plain": [
-              "(81306, 1)"
-            ]
-          },
-          "metadata": {},
-          "execution_count": 27
-        }
-      ]
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "for i in range(10):\n",
-        "  g2 = g.chain([n({'id': 17116707}), e_forward(hops=1)])\n",
-        "g2._nodes.shape, g2._edges.shape"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "yUaRfw4FHGMb",
-        "outputId": "3945cc5a-c36c-451b-ac95-8af992a3546f"
-      },
-      "execution_count": 29,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "CPU times: user 11.8 s, sys: 8.4 s, total: 20.2 s\n",
-            "Wall time: 23 s\n"
-          ]
-        },
-        {
-          "output_type": "execute_result",
-          "data": {
-            "text/plain": [
-              "((140, 1), (615, 2))"
-            ]
-          },
-          "metadata": {},
-          "execution_count": 29
-        }
-      ]
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "g_gdf = g.nodes(lambda g: cudf.DataFrame(g._nodes)).edges(lambda g: cudf.DataFrame(g._edges))\n",
-        "for i in range(10):\n",
-        "  out = g_gdf.chain([n({'id': 17116707}), e_forward(hops=1)])._nodes\n",
-        "print(out.shape)\n",
-        "del g_gdf\n",
-        "del out"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "5hM4NBu2_eks",
-        "outputId": "54505262-4871-44ee-e5e4-ad7ab32c13c2"
-      },
-      "execution_count": 30,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "(140, 1)\n",
-            "CPU times: user 1.33 s, sys: 46.6 ms, total: 1.38 s\n",
-            "Wall time: 1.63 s\n"
-          ]
-        }
-      ]
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "for i in range(10):\n",
-        "  out = g.chain([n({'id': 17116707}), e_forward(hops=2)])\n",
-        "print(out._nodes.shape, out._edges.shape)"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "m2-MxD5lHX6u",
-        "outputId": "e89b9d4b-6c04-45c7-9e7f-cbdbbe0a4730"
-      },
-      "execution_count": 31,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "(2345, 1) (68536, 2)\n",
-            "CPU times: user 13.3 s, sys: 8.05 s, total: 21.4 s\n",
-            "Wall time: 21.6 s\n"
-          ]
-        }
-      ]
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "g_gdf = g.nodes(lambda g: cudf.DataFrame(g._nodes)).edges(lambda g: cudf.DataFrame(g._edges))\n",
-        "for i in range(10):\n",
-        "  out = g_gdf.chain([n({'id': 17116707}), e_forward(hops=2)])._nodes\n",
-        "print(out.shape)\n",
-        "del g_gdf\n",
-        "del out"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "7EQSRbIqLaGw",
-        "outputId": "60c00a03-9e7b-46b5-fce3-f4f567a09430"
-      },
-      "execution_count": 36,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "(2345, 1)\n",
-            "CPU times: user 1.67 s, sys: 55.8 ms, total: 1.72 s\n",
-            "Wall time: 1.75 s\n"
-          ]
-        }
-      ]
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "for i in range(10):\n",
-        "  out = g.chain([n({'id': 17116707}), e_forward(hops=8)])\n",
-        "print(out._nodes.shape, out._edges.shape)"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "hh6WnjI3ITpB",
-        "outputId": "33138efe-a581-49ed-b2b4-247f8e9bdc09"
-      },
-      "execution_count": 37,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "(81304, 1) (2417796, 2)\n",
-            "CPU times: user 1min 56s, sys: 17.1 s, total: 2min 13s\n",
-            "Wall time: 2min 22s\n"
-          ]
-        }
-      ]
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "g_gdf = g.nodes(lambda g: cudf.DataFrame(g._nodes)).edges(lambda g: cudf.DataFrame(g._edges))\n",
-        "for i in range(10):\n",
-        "  out = g_gdf.chain([n({'id': 17116707}), e_forward(hops=8)])._nodes\n",
-        "print(out.shape)\n",
-        "del g_gdf\n",
-        "del out"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "7jFFVUenM87j",
-        "outputId": "2cceb720-9de3-488e-8b74-b820fd06e6c1"
-      },
-      "execution_count": 38,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "(81304, 1)\n",
-            "CPU times: user 5.3 s, sys: 1.48 s, total: 6.78 s\n",
-            "Wall time: 7.89 s\n"
-          ]
-        }
-      ]
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "start_nodes = pd.DataFrame({g._node: [17116707]})\n",
-        "for i in range(10):\n",
-        "  g2 = g.hop(\n",
-        "      nodes=start_nodes,\n",
-        "      direction='forward',\n",
-        "      hops=1)\n",
-        "print(g2._nodes.shape, g2._edges.shape)"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "_5LD0bZB_lU4",
-        "outputId": "bc31bd03-e79f-46d2-ea8f-3b01d9ef39a2"
-      },
-      "execution_count": 39,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "(0, 1) (0, 2)\n",
-            "CPU times: user 2.58 s, sys: 1.59 s, total: 4.17 s\n",
-            "Wall time: 6.02 s\n"
-          ]
-        }
-      ]
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "start_nodes = cudf.DataFrame({g._node: [17116707]})\n",
-        "g_gdf = g.nodes(cudf.from_pandas(g._nodes)).edges(cudf.from_pandas(g._edges))\n",
-        "for i in range(10):\n",
-        "  g2 = g_gdf.hop(\n",
-        "      nodes=start_nodes,\n",
-        "      direction='forward',\n",
-        "      hops=5)\n",
-        "print(g2._nodes.shape, g2._edges.shape)\n",
-        "del start_nodes\n",
-        "del g_gdf\n",
-        "del g2"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "M_rHjqtvACQw",
-        "outputId": "8d3e308e-b1e2-452b-f402-573be0dd5b58"
-      },
-      "execution_count": 44,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "(61827, 1) (1473599, 2)\n",
-            "CPU times: user 822 ms, sys: 179 ms, total: 1 s\n",
-            "Wall time: 997 ms\n"
-          ]
-        }
-      ]
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "start_nodes = pd.DataFrame({g._node: [17116707]})\n",
-        "for i in range(10):\n",
-        "  g2 = g.hop(\n",
-        "      nodes=start_nodes,\n",
-        "      direction='forward',\n",
-        "      hops=2)\n",
-        "print(g2._nodes.shape, g2._edges.shape)"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "0zEIucaCAbj_",
-        "outputId": "83e64b0f-2b3a-4e4b-d189-3e6a8ef78f53"
-      },
-      "execution_count": 40,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "(2345, 1) (68536, 2)\n",
-            "CPU times: user 8.93 s, sys: 5.92 s, total: 14.9 s\n",
-            "Wall time: 15.8 s\n"
-          ]
-        }
-      ]
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "start_nodes = cudf.DataFrame({g._node: [17116707]})\n",
-        "g_gdf = g.nodes(cudf.from_pandas(g._nodes)).edges(cudf.from_pandas(g._edges))\n",
-        "for i in range(10):\n",
-        "  g2 = g_gdf.hop(\n",
-        "      nodes=start_nodes,\n",
-        "      direction='forward',\n",
-        "      hops=2)\n",
-        "print(g2._nodes.shape, g2._edges.shape)\n",
-        "del start_nodes\n",
-        "del g_gdf\n",
-        "del g2"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "LKJh5gRtAdIj",
-        "outputId": "e3c7883d-74c0-4d55-b238-88457296c6bc"
-      },
-      "execution_count": 41,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "(2345, 1) (68536, 2)\n",
-            "CPU times: user 374 ms, sys: 6.92 ms, total: 381 ms\n",
-            "Wall time: 379 ms\n"
-          ]
-        }
-      ]
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "start_nodes = pd.DataFrame({g._node: [17116707]})\n",
-        "for i in range(10):\n",
-        "  g2 = g.hop(\n",
-        "      nodes=start_nodes,\n",
-        "      direction='forward',\n",
-        "      hops=8)\n",
-        "print(g2._nodes.shape, g2._edges.shape)"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "JZwxdofNAfmb",
-        "outputId": "2731be4c-75d9-47f4-8602-4f2d6cb2ddac"
-      },
-      "execution_count": 42,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "(81304, 1) (2417796, 2)\n",
-            "CPU times: user 38.8 s, sys: 8.7 s, total: 47.5 s\n",
-            "Wall time: 48.2 s\n"
-          ]
-        }
-      ]
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "start_nodes = cudf.DataFrame({g._node: [17116707]})\n",
-        "g_gdf = g.nodes(cudf.from_pandas(g._nodes)).edges(cudf.from_pandas(g._edges))\n",
-        "for i in range(10):\n",
-        "  g2 = g_gdf.hop(\n",
-        "      nodes=start_nodes,\n",
-        "      direction='forward',\n",
-        "      hops=8)\n",
-        "print(g2._nodes.shape, g2._edges.shape)\n",
-        "del start_nodes\n",
-        "del g_gdf\n",
-        "del g2"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "9o_og8bSAhe3",
-        "outputId": "dd3e4f8f-f426-4705-98c4-60f1912ba28a"
-      },
-      "execution_count": 43,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "(81304, 1) (2417796, 2)\n",
-            "CPU times: user 1.8 s, sys: 506 ms, total: 2.3 s\n",
-            "Wall time: 2.3 s\n"
-          ]
-        }
-      ]
-    },
-    {
-      "cell_type": "markdown",
-      "source": [
-        "### GPlus\n",
-        "\n",
-        "- edges: 30494866\n",
-        "- nodes: 107614"
-      ],
-      "metadata": {
-        "id": "9dZzAAVONCD2"
-      }
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "! wget https://snap.stanford.edu/data/gplus_combined.txt.gz"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "-nhWGNekKpcZ",
-        "outputId": "e2175290-337c-4faa-e5d8-4bc401583326"
-      },
-      "execution_count": 4,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "--2023-12-26 18:36:29--  https://snap.stanford.edu/data/gplus_combined.txt.gz\n",
-            "Resolving snap.stanford.edu (snap.stanford.edu)... 171.64.75.80\n",
-            "Connecting to snap.stanford.edu (snap.stanford.edu)|171.64.75.80|:443... connected.\n",
-            "HTTP request sent, awaiting response... 200 OK\n",
-            "Length: 398930514 (380M) [application/x-gzip]\n",
-            "Saving to: ‘gplus_combined.txt.gz’\n",
-            "\n",
-            "gplus_combined.txt. 100%[===================>] 380.45M  34.7MB/s    in 9.6s    \n",
-            "\n",
-            "2023-12-26 18:36:39 (39.7 MB/s) - ‘gplus_combined.txt.gz’ saved [398930514/398930514]\n",
-            "\n"
-          ]
-        }
-      ]
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "! gunzip gplus_combined.txt.gz"
-      ],
-      "metadata": {
-        "id": "g5wgA_c2KqwJ"
-      },
-      "execution_count": 5,
-      "outputs": []
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "ge_df = pd.read_csv('gplus_combined.txt', sep=' ', names=['s', 'd'])\n",
-        "print(ge_df.shape)\n",
-        "ge_df.head(5)"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/",
-          "height": 258
-        },
-        "id": "52hgDbr0Kti6",
-        "outputId": "217203fc-7095-4784-c4c4-d46ee9c78808"
-      },
-      "execution_count": 6,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "(30494866, 2)\n",
-            "CPU times: user 16 s, sys: 1.45 s, total: 17.5 s\n",
-            "Wall time: 22.5 s\n"
-          ]
-        },
-        {
-          "output_type": "execute_result",
-          "data": {
-            "text/plain": [
-              "                       s                      d\n",
-              "0  116374117927631468606  101765416973555767821\n",
-              "1  112188647432305746617  107727150903234299458\n",
-              "2  116719211656774388392  100432456209427807893\n",
-              "3  117421021456205115327  101096322838605097368\n",
-              "4  116407635616074189669  113556266482860931616"
-            ],
-            "text/html": [
-              "\n",
-              "  <div id=\"df-0d42e599-73d6-4059-91f3-83f525b5891f\" class=\"colab-df-container\">\n",
-              "    <div>\n",
-              "<style scoped>\n",
-              "    .dataframe tbody tr th:only-of-type {\n",
-              "        vertical-align: middle;\n",
-              "    }\n",
-              "\n",
-              "    .dataframe tbody tr th {\n",
-              "        vertical-align: top;\n",
-              "    }\n",
-              "\n",
-              "    .dataframe thead th {\n",
-              "        text-align: right;\n",
-              "    }\n",
-              "</style>\n",
-              "<table border=\"1\" class=\"dataframe\">\n",
-              "  <thead>\n",
-              "    <tr style=\"text-align: right;\">\n",
-              "      <th></th>\n",
-              "      <th>s</th>\n",
-              "      <th>d</th>\n",
-              "    </tr>\n",
-              "  </thead>\n",
-              "  <tbody>\n",
-              "    <tr>\n",
-              "      <th>0</th>\n",
-              "      <td>116374117927631468606</td>\n",
-              "      <td>101765416973555767821</td>\n",
-              "    </tr>\n",
-              "    <tr>\n",
-              "      <th>1</th>\n",
-              "      <td>112188647432305746617</td>\n",
-              "      <td>107727150903234299458</td>\n",
-              "    </tr>\n",
-              "    <tr>\n",
-              "      <th>2</th>\n",
-              "      <td>116719211656774388392</td>\n",
-              "      <td>100432456209427807893</td>\n",
-              "    </tr>\n",
-              "    <tr>\n",
-              "      <th>3</th>\n",
-              "      <td>117421021456205115327</td>\n",
-              "      <td>101096322838605097368</td>\n",
-              "    </tr>\n",
-              "    <tr>\n",
-              "      <th>4</th>\n",
-              "      <td>116407635616074189669</td>\n",
-              "      <td>113556266482860931616</td>\n",
-              "    </tr>\n",
-              "  </tbody>\n",
-              "</table>\n",
-              "</div>\n",
-              "    <div class=\"colab-df-buttons\">\n",
-              "\n",
-              "  <div class=\"colab-df-container\">\n",
-              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-0d42e599-73d6-4059-91f3-83f525b5891f')\"\n",
-              "            title=\"Convert this dataframe to an interactive table.\"\n",
-              "            style=\"display:none;\">\n",
-              "\n",
-              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
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-              "  </svg>\n",
-              "    </button>\n",
-              "\n",
-              "  <style>\n",
-              "    .colab-df-container {\n",
-              "      display:flex;\n",
-              "      gap: 12px;\n",
-              "    }\n",
-              "\n",
-              "    .colab-df-convert {\n",
-              "      background-color: #E8F0FE;\n",
-              "      border: none;\n",
-              "      border-radius: 50%;\n",
-              "      cursor: pointer;\n",
-              "      display: none;\n",
-              "      fill: #1967D2;\n",
-              "      height: 32px;\n",
-              "      padding: 0 0 0 0;\n",
-              "      width: 32px;\n",
-              "    }\n",
-              "\n",
-              "    .colab-df-convert:hover {\n",
-              "      background-color: #E2EBFA;\n",
-              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
-              "      fill: #174EA6;\n",
-              "    }\n",
-              "\n",
-              "    .colab-df-buttons div {\n",
-              "      margin-bottom: 4px;\n",
-              "    }\n",
-              "\n",
-              "    [theme=dark] .colab-df-convert {\n",
-              "      background-color: #3B4455;\n",
-              "      fill: #D2E3FC;\n",
-              "    }\n",
-              "\n",
-              "    [theme=dark] .colab-df-convert:hover {\n",
-              "      background-color: #434B5C;\n",
-              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
-              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
-              "      fill: #FFFFFF;\n",
-              "    }\n",
-              "  </style>\n",
-              "\n",
-              "    <script>\n",
-              "      const buttonEl =\n",
-              "        document.querySelector('#df-0d42e599-73d6-4059-91f3-83f525b5891f button.colab-df-convert');\n",
-              "      buttonEl.style.display =\n",
-              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
-              "\n",
-              "      async function convertToInteractive(key) {\n",
-              "        const element = document.querySelector('#df-0d42e599-73d6-4059-91f3-83f525b5891f');\n",
-              "        const dataTable =\n",
-              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
-              "                                                    [key], {});\n",
-              "        if (!dataTable) return;\n",
-              "\n",
-              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
-              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
-              "          + ' to learn more about interactive tables.';\n",
-              "        element.innerHTML = '';\n",
-              "        dataTable['output_type'] = 'display_data';\n",
-              "        await google.colab.output.renderOutput(dataTable, element);\n",
-              "        const docLink = document.createElement('div');\n",
-              "        docLink.innerHTML = docLinkHtml;\n",
-              "        element.appendChild(docLink);\n",
-              "      }\n",
-              "    </script>\n",
-              "  </div>\n",
-              "\n",
-              "\n",
-              "<div id=\"df-623952d7-77ea-4e29-b39b-c80edd4a7219\">\n",
-              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-623952d7-77ea-4e29-b39b-c80edd4a7219')\"\n",
-              "            title=\"Suggest charts\"\n",
-              "            style=\"display:none;\">\n",
-              "\n",
-              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
-              "     width=\"24px\">\n",
-              "    <g>\n",
-              "        <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
-              "    </g>\n",
-              "</svg>\n",
-              "  </button>\n",
-              "\n",
-              "<style>\n",
-              "  .colab-df-quickchart {\n",
-              "      --bg-color: #E8F0FE;\n",
-              "      --fill-color: #1967D2;\n",
-              "      --hover-bg-color: #E2EBFA;\n",
-              "      --hover-fill-color: #174EA6;\n",
-              "      --disabled-fill-color: #AAA;\n",
-              "      --disabled-bg-color: #DDD;\n",
-              "  }\n",
-              "\n",
-              "  [theme=dark] .colab-df-quickchart {\n",
-              "      --bg-color: #3B4455;\n",
-              "      --fill-color: #D2E3FC;\n",
-              "      --hover-bg-color: #434B5C;\n",
-              "      --hover-fill-color: #FFFFFF;\n",
-              "      --disabled-bg-color: #3B4455;\n",
-              "      --disabled-fill-color: #666;\n",
-              "  }\n",
-              "\n",
-              "  .colab-df-quickchart {\n",
-              "    background-color: var(--bg-color);\n",
-              "    border: none;\n",
-              "    border-radius: 50%;\n",
-              "    cursor: pointer;\n",
-              "    display: none;\n",
-              "    fill: var(--fill-color);\n",
-              "    height: 32px;\n",
-              "    padding: 0;\n",
-              "    width: 32px;\n",
-              "  }\n",
-              "\n",
-              "  .colab-df-quickchart:hover {\n",
-              "    background-color: var(--hover-bg-color);\n",
-              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
-              "    fill: var(--button-hover-fill-color);\n",
-              "  }\n",
-              "\n",
-              "  .colab-df-quickchart-complete:disabled,\n",
-              "  .colab-df-quickchart-complete:disabled:hover {\n",
-              "    background-color: var(--disabled-bg-color);\n",
-              "    fill: var(--disabled-fill-color);\n",
-              "    box-shadow: none;\n",
-              "  }\n",
-              "\n",
-              "  .colab-df-spinner {\n",
-              "    border: 2px solid var(--fill-color);\n",
-              "    border-color: transparent;\n",
-              "    border-bottom-color: var(--fill-color);\n",
-              "    animation:\n",
-              "      spin 1s steps(1) infinite;\n",
-              "  }\n",
-              "\n",
-              "  @keyframes spin {\n",
-              "    0% {\n",
-              "      border-color: transparent;\n",
-              "      border-bottom-color: var(--fill-color);\n",
-              "      border-left-color: var(--fill-color);\n",
-              "    }\n",
-              "    20% {\n",
-              "      border-color: transparent;\n",
-              "      border-left-color: var(--fill-color);\n",
-              "      border-top-color: var(--fill-color);\n",
-              "    }\n",
-              "    30% {\n",
-              "      border-color: transparent;\n",
-              "      border-left-color: var(--fill-color);\n",
-              "      border-top-color: var(--fill-color);\n",
-              "      border-right-color: var(--fill-color);\n",
-              "    }\n",
-              "    40% {\n",
-              "      border-color: transparent;\n",
-              "      border-right-color: var(--fill-color);\n",
-              "      border-top-color: var(--fill-color);\n",
-              "    }\n",
-              "    60% {\n",
-              "      border-color: transparent;\n",
-              "      border-right-color: var(--fill-color);\n",
-              "    }\n",
-              "    80% {\n",
-              "      border-color: transparent;\n",
-              "      border-right-color: var(--fill-color);\n",
-              "      border-bottom-color: var(--fill-color);\n",
-              "    }\n",
-              "    90% {\n",
-              "      border-color: transparent;\n",
-              "      border-bottom-color: var(--fill-color);\n",
-              "    }\n",
-              "  }\n",
-              "</style>\n",
-              "\n",
-              "  <script>\n",
-              "    async function quickchart(key) {\n",
-              "      const quickchartButtonEl =\n",
-              "        document.querySelector('#' + key + ' button');\n",
-              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
-              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
-              "      try {\n",
-              "        const charts = await google.colab.kernel.invokeFunction(\n",
-              "            'suggestCharts', [key], {});\n",
-              "      } catch (error) {\n",
-              "        console.error('Error during call to suggestCharts:', error);\n",
-              "      }\n",
-              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
-              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
-              "    }\n",
-              "    (() => {\n",
-              "      let quickchartButtonEl =\n",
-              "        document.querySelector('#df-623952d7-77ea-4e29-b39b-c80edd4a7219 button');\n",
-              "      quickchartButtonEl.style.display =\n",
-              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
-              "    })();\n",
-              "  </script>\n",
-              "</div>\n",
-              "    </div>\n",
-              "  </div>\n"
-            ]
-          },
-          "metadata": {},
-          "execution_count": 6
-        }
-      ]
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "gg = graphistry.edges(ge_df, 's', 'd').materialize_nodes()\n",
-        "gg = graphistry.edges(ge_df, 's', 'd').nodes(gg._nodes, 'id')\n",
-        "print(gg._edges.shape, gg._nodes.shape)\n",
-        "gg._nodes.head(5)"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/",
-          "height": 258
-        },
-        "id": "w5YkN-nLK6UV",
-        "outputId": "dc98380d-54c2-4b36-c56e-5e8401c4ffa4"
-      },
-      "execution_count": 7,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "(30494866, 2) (107614, 1)\n",
-            "CPU times: user 4.49 s, sys: 1.25 s, total: 5.74 s\n",
-            "Wall time: 5.97 s\n"
-          ]
-        },
-        {
-          "output_type": "execute_result",
-          "data": {
-            "text/plain": [
-              "                      id\n",
-              "0  116374117927631468606\n",
-              "1  112188647432305746617\n",
-              "2  116719211656774388392\n",
-              "3  117421021456205115327\n",
-              "4  116407635616074189669"
+              "                                      0        1\n",
+              "hops                                  2        5\n",
+              "CPU n_notation time (s)         11.8076  25.4098\n",
+              "GPU n_notation time (s)         10.3238  14.4829\n",
+              "n_notation speedup               1.1437   1.7545\n",
+              "CPU source_node_match time (s)  12.0969  10.2662\n",
+              "GPU source_node_match time (s)  11.2681   11.199\n",
+              "source_node_match speedup        1.0736   0.9167"
             ],
             "text/html": [
               "\n",
-              "  <div id=\"df-c1d2fbc6-366f-4484-8c81-15eaec2f8e5e\" class=\"colab-df-container\">\n",
+              "  <div id=\"df-ad61764f-372d-4232-80b8-9453e9ea31e4\" class=\"colab-df-container\">\n",
               "    <div>\n",
               "<style scoped>\n",
               "    .dataframe tbody tr th:only-of-type {\n",
@@ -2211,29 +996,45 @@
               "  <thead>\n",
               "    <tr style=\"text-align: right;\">\n",
               "      <th></th>\n",
-              "      <th>id</th>\n",
+              "      <th>0</th>\n",
+              "      <th>1</th>\n",
               "    </tr>\n",
               "  </thead>\n",
               "  <tbody>\n",
               "    <tr>\n",
-              "      <th>0</th>\n",
-              "      <td>116374117927631468606</td>\n",
+              "      <th>hops</th>\n",
+              "      <td>2</td>\n",
+              "      <td>5</td>\n",
               "    </tr>\n",
               "    <tr>\n",
-              "      <th>1</th>\n",
-              "      <td>112188647432305746617</td>\n",
+              "      <th>CPU n_notation time (s)</th>\n",
+              "      <td>11.8076</td>\n",
+              "      <td>25.4098</td>\n",
               "    </tr>\n",
               "    <tr>\n",
-              "      <th>2</th>\n",
-              "      <td>116719211656774388392</td>\n",
+              "      <th>GPU n_notation time (s)</th>\n",
+              "      <td>10.3238</td>\n",
+              "      <td>14.4829</td>\n",
               "    </tr>\n",
               "    <tr>\n",
-              "      <th>3</th>\n",
-              "      <td>117421021456205115327</td>\n",
+              "      <th>n_notation speedup</th>\n",
+              "      <td>1.1437</td>\n",
+              "      <td>1.7545</td>\n",
               "    </tr>\n",
               "    <tr>\n",
-              "      <th>4</th>\n",
-              "      <td>116407635616074189669</td>\n",
+              "      <th>CPU source_node_match time (s)</th>\n",
+              "      <td>12.0969</td>\n",
+              "      <td>10.2662</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>GPU source_node_match time (s)</th>\n",
+              "      <td>11.2681</td>\n",
+              "      <td>11.199</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>source_node_match speedup</th>\n",
+              "      <td>1.0736</td>\n",
+              "      <td>0.9167</td>\n",
               "    </tr>\n",
               "  </tbody>\n",
               "</table>\n",
@@ -2241,7 +1042,7 @@
               "    <div class=\"colab-df-buttons\">\n",
               "\n",
               "  <div class=\"colab-df-container\">\n",
-              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-c1d2fbc6-366f-4484-8c81-15eaec2f8e5e')\"\n",
+              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-ad61764f-372d-4232-80b8-9453e9ea31e4')\"\n",
               "            title=\"Convert this dataframe to an interactive table.\"\n",
               "            style=\"display:none;\">\n",
               "\n",
@@ -2293,12 +1094,12 @@
               "\n",
               "    <script>\n",
               "      const buttonEl =\n",
-              "        document.querySelector('#df-c1d2fbc6-366f-4484-8c81-15eaec2f8e5e button.colab-df-convert');\n",
+              "        document.querySelector('#df-ad61764f-372d-4232-80b8-9453e9ea31e4 button.colab-df-convert');\n",
               "      buttonEl.style.display =\n",
               "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
               "\n",
               "      async function convertToInteractive(key) {\n",
-              "        const element = document.querySelector('#df-c1d2fbc6-366f-4484-8c81-15eaec2f8e5e');\n",
+              "        const element = document.querySelector('#df-ad61764f-372d-4232-80b8-9453e9ea31e4');\n",
               "        const dataTable =\n",
               "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
               "                                                    [key], {});\n",
@@ -2318,8 +1119,8 @@
               "  </div>\n",
               "\n",
               "\n",
-              "<div id=\"df-df8cfeb9-5932-49da-82f5-2c8dc224b580\">\n",
-              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-df8cfeb9-5932-49da-82f5-2c8dc224b580')\"\n",
+              "<div id=\"df-0a712080-5f34-4df9-a79a-4e3af31230b0\">\n",
+              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-0a712080-5f34-4df9-a79a-4e3af31230b0')\"\n",
               "            title=\"Suggest charts\"\n",
               "            style=\"display:none;\">\n",
               "\n",
@@ -2379,1134 +1180,1011 @@
               "    border: 2px solid var(--fill-color);\n",
               "    border-color: transparent;\n",
               "    border-bottom-color: var(--fill-color);\n",
-              "    animation:\n",
-              "      spin 1s steps(1) infinite;\n",
-              "  }\n",
-              "\n",
-              "  @keyframes spin {\n",
-              "    0% {\n",
-              "      border-color: transparent;\n",
-              "      border-bottom-color: var(--fill-color);\n",
-              "      border-left-color: var(--fill-color);\n",
-              "    }\n",
-              "    20% {\n",
-              "      border-color: transparent;\n",
-              "      border-left-color: var(--fill-color);\n",
-              "      border-top-color: var(--fill-color);\n",
-              "    }\n",
-              "    30% {\n",
-              "      border-color: transparent;\n",
-              "      border-left-color: var(--fill-color);\n",
-              "      border-top-color: var(--fill-color);\n",
-              "      border-right-color: var(--fill-color);\n",
-              "    }\n",
-              "    40% {\n",
-              "      border-color: transparent;\n",
-              "      border-right-color: var(--fill-color);\n",
-              "      border-top-color: var(--fill-color);\n",
-              "    }\n",
-              "    60% {\n",
-              "      border-color: transparent;\n",
-              "      border-right-color: var(--fill-color);\n",
-              "    }\n",
-              "    80% {\n",
-              "      border-color: transparent;\n",
-              "      border-right-color: var(--fill-color);\n",
-              "      border-bottom-color: var(--fill-color);\n",
-              "    }\n",
-              "    90% {\n",
-              "      border-color: transparent;\n",
-              "      border-bottom-color: var(--fill-color);\n",
-              "    }\n",
-              "  }\n",
-              "</style>\n",
-              "\n",
-              "  <script>\n",
-              "    async function quickchart(key) {\n",
-              "      const quickchartButtonEl =\n",
-              "        document.querySelector('#' + key + ' button');\n",
-              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
-              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
-              "      try {\n",
-              "        const charts = await google.colab.kernel.invokeFunction(\n",
-              "            'suggestCharts', [key], {});\n",
-              "      } catch (error) {\n",
-              "        console.error('Error during call to suggestCharts:', error);\n",
-              "      }\n",
-              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
-              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
-              "    }\n",
-              "    (() => {\n",
-              "      let quickchartButtonEl =\n",
-              "        document.querySelector('#df-df8cfeb9-5932-49da-82f5-2c8dc224b580 button');\n",
-              "      quickchartButtonEl.style.display =\n",
-              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
-              "    })();\n",
-              "  </script>\n",
-              "</div>\n",
-              "    </div>\n",
-              "  </div>\n"
-            ]
-          },
-          "metadata": {},
-          "execution_count": 7
-        }
-      ]
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "gg.chain([ n({'id': '116374117927631468606'})])._nodes"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/",
-          "height": 115
-        },
-        "id": "NKtz54uELX-8",
-        "outputId": "5d8f3eef-893d-47cc-e7a9-c5cbfec8270c"
-      },
-      "execution_count": 49,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "CPU times: user 534 ms, sys: 598 ms, total: 1.13 s\n",
-            "Wall time: 1.65 s\n"
-          ]
-        },
-        {
-          "output_type": "execute_result",
-          "data": {
-            "text/plain": [
-              "                      id\n",
-              "0  116374117927631468606"
-            ],
-            "text/html": [
-              "\n",
-              "  <div id=\"df-9c79ab83-1d00-433a-ac53-258bafc7faac\" class=\"colab-df-container\">\n",
-              "    <div>\n",
-              "<style scoped>\n",
-              "    .dataframe tbody tr th:only-of-type {\n",
-              "        vertical-align: middle;\n",
-              "    }\n",
-              "\n",
-              "    .dataframe tbody tr th {\n",
-              "        vertical-align: top;\n",
-              "    }\n",
-              "\n",
-              "    .dataframe thead th {\n",
-              "        text-align: right;\n",
-              "    }\n",
-              "</style>\n",
-              "<table border=\"1\" class=\"dataframe\">\n",
-              "  <thead>\n",
-              "    <tr style=\"text-align: right;\">\n",
-              "      <th></th>\n",
-              "      <th>id</th>\n",
-              "    </tr>\n",
-              "  </thead>\n",
-              "  <tbody>\n",
-              "    <tr>\n",
-              "      <th>0</th>\n",
-              "      <td>116374117927631468606</td>\n",
-              "    </tr>\n",
-              "  </tbody>\n",
-              "</table>\n",
-              "</div>\n",
-              "    <div class=\"colab-df-buttons\">\n",
-              "\n",
-              "  <div class=\"colab-df-container\">\n",
-              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-9c79ab83-1d00-433a-ac53-258bafc7faac')\"\n",
-              "            title=\"Convert this dataframe to an interactive table.\"\n",
-              "            style=\"display:none;\">\n",
-              "\n",
-              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
-              "    <path d=\"M120-120v-720h720v720H120Zm60-500h600v-160H180v160Zm220 220h160v-160H400v160Zm0 220h160v-160H400v160ZM180-400h160v-160H180v160Zm440 0h160v-160H620v160ZM180-180h160v-160H180v160Zm440 0h160v-160H620v160Z\"/>\n",
-              "  </svg>\n",
-              "    </button>\n",
+              "    animation:\n",
+              "      spin 1s steps(1) infinite;\n",
+              "  }\n",
               "\n",
-              "  <style>\n",
-              "    .colab-df-container {\n",
-              "      display:flex;\n",
-              "      gap: 12px;\n",
+              "  @keyframes spin {\n",
+              "    0% {\n",
+              "      border-color: transparent;\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "      border-left-color: var(--fill-color);\n",
               "    }\n",
-              "\n",
-              "    .colab-df-convert {\n",
-              "      background-color: #E8F0FE;\n",
-              "      border: none;\n",
-              "      border-radius: 50%;\n",
-              "      cursor: pointer;\n",
-              "      display: none;\n",
-              "      fill: #1967D2;\n",
-              "      height: 32px;\n",
-              "      padding: 0 0 0 0;\n",
-              "      width: 32px;\n",
+              "    20% {\n",
+              "      border-color: transparent;\n",
+              "      border-left-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
               "    }\n",
-              "\n",
-              "    .colab-df-convert:hover {\n",
-              "      background-color: #E2EBFA;\n",
-              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
-              "      fill: #174EA6;\n",
+              "    30% {\n",
+              "      border-color: transparent;\n",
+              "      border-left-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "      border-right-color: var(--fill-color);\n",
               "    }\n",
-              "\n",
-              "    .colab-df-buttons div {\n",
-              "      margin-bottom: 4px;\n",
+              "    40% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
               "    }\n",
-              "\n",
-              "    [theme=dark] .colab-df-convert {\n",
-              "      background-color: #3B4455;\n",
-              "      fill: #D2E3FC;\n",
+              "    60% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
               "    }\n",
-              "\n",
-              "    [theme=dark] .colab-df-convert:hover {\n",
-              "      background-color: #434B5C;\n",
-              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
-              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
-              "      fill: #FFFFFF;\n",
+              "    80% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "      border-bottom-color: var(--fill-color);\n",
               "    }\n",
-              "  </style>\n",
-              "\n",
-              "    <script>\n",
-              "      const buttonEl =\n",
-              "        document.querySelector('#df-9c79ab83-1d00-433a-ac53-258bafc7faac button.colab-df-convert');\n",
-              "      buttonEl.style.display =\n",
-              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
-              "\n",
-              "      async function convertToInteractive(key) {\n",
-              "        const element = document.querySelector('#df-9c79ab83-1d00-433a-ac53-258bafc7faac');\n",
-              "        const dataTable =\n",
-              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
-              "                                                    [key], {});\n",
-              "        if (!dataTable) return;\n",
+              "    90% {\n",
+              "      border-color: transparent;\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "    }\n",
+              "  }\n",
+              "</style>\n",
               "\n",
-              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
-              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
-              "          + ' to learn more about interactive tables.';\n",
-              "        element.innerHTML = '';\n",
-              "        dataTable['output_type'] = 'display_data';\n",
-              "        await google.colab.output.renderOutput(dataTable, element);\n",
-              "        const docLink = document.createElement('div');\n",
-              "        docLink.innerHTML = docLinkHtml;\n",
-              "        element.appendChild(docLink);\n",
+              "  <script>\n",
+              "    async function quickchart(key) {\n",
+              "      const quickchartButtonEl =\n",
+              "        document.querySelector('#' + key + ' button');\n",
+              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
+              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
+              "      try {\n",
+              "        const charts = await google.colab.kernel.invokeFunction(\n",
+              "            'suggestCharts', [key], {});\n",
+              "      } catch (error) {\n",
+              "        console.error('Error during call to suggestCharts:', error);\n",
               "      }\n",
-              "    </script>\n",
-              "  </div>\n",
+              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
+              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
+              "    }\n",
+              "    (() => {\n",
+              "      let quickchartButtonEl =\n",
+              "        document.querySelector('#df-0a712080-5f34-4df9-a79a-4e3af31230b0 button');\n",
+              "      quickchartButtonEl.style.display =\n",
+              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
+              "    })();\n",
+              "  </script>\n",
+              "</div>\n",
               "\n",
               "    </div>\n",
               "  </div>\n"
-            ]
-          },
-          "metadata": {},
-          "execution_count": 49
-        }
-      ]
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "out = gg.chain([ n({'id': '116374117927631468606'}), e_forward(hops=1)])._nodes\n",
-        "out.shape"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "iNWdi00VLmZG",
-        "outputId": "ecfb56a6-c564-4bf6-f43f-2c95a103f4be"
-      },
-      "execution_count": null,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "CPU times: user 27.5 s, sys: 11.1 s, total: 38.5 s\n",
-            "Wall time: 39.5 s\n"
-          ]
-        },
-        {
-          "output_type": "execute_result",
-          "data": {
-            "text/plain": [
-              "(1473, 1)"
-            ]
-          },
-          "metadata": {},
-          "execution_count": 75
-        }
-      ]
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "gg_gdf = gg.nodes(lambda g: cudf.DataFrame(g._nodes)).edges(lambda g: cudf.DataFrame(g._edges))\n",
-        "out = gg_gdf.chain([ n({'id': '116374117927631468606'}), e_forward(hops=1)])\n",
-        "print(out._nodes.shape, out._edges.shape)\n",
-        "del gg_gdf\n",
-        "del out"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "Q6p3h6uCOABh",
-        "outputId": "817fc80f-ef5d-4070-eb48-a12344be709c"
-      },
-      "execution_count": null,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "(1473, 1) (13375, 2)\n",
-            "CPU times: user 4.57 s, sys: 2.11 s, total: 6.68 s\n",
-            "Wall time: 7.63 s\n"
-          ]
-        }
-      ]
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "out = gg.chain([ n({'id': '116374117927631468606'}), e_forward(hops=2)])._nodes\n",
-        "out.shape"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "6UdCcMdqLw-P",
-        "outputId": "70742c79-b22b-4db2-c548-cb1e25d572eb"
-      },
-      "execution_count": null,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "CPU times: user 45.8 s, sys: 17 s, total: 1min 2s\n",
-            "Wall time: 1min 5s\n"
-          ]
-        },
-        {
-          "output_type": "execute_result",
-          "data": {
-            "text/plain": [
-              "(44073, 1)"
-            ]
+            ],
+            "application/vnd.google.colaboratory.intrinsic+json": {
+              "type": "dataframe",
+              "summary": "{\n  \"name\": \"results_df\",\n  \"rows\": 7,\n  \"fields\": [\n    {\n      \"column\": 0,\n      \"properties\": {\n        \"dtype\": \"date\",\n        \"min\": 1.0736,\n        \"max\": 12.0969,\n        \"num_unique_values\": 7,\n        \"samples\": [\n          2,\n          11.8076,\n          11.2681\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": 1,\n      \"properties\": {\n        \"dtype\": \"date\",\n        \"min\": 0.9167,\n        \"max\": 25.4098,\n        \"num_unique_values\": 7,\n        \"samples\": [\n          5,\n          25.4098,\n          11.199\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
+            }
           },
           "metadata": {},
-          "execution_count": 77
-        }
-      ]
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "gg_gdf = gg.nodes(lambda g: cudf.DataFrame(g._nodes)).edges(lambda g: cudf.DataFrame(g._edges))\n",
-        "out = gg_gdf.chain([ n({'id': '116374117927631468606'}), e_forward(hops=2)])\n",
-        "print(out._nodes.shape, out._edges.shape)\n",
-        "del gg_gdf\n",
-        "del out"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "QElqatDyNYCS",
-        "outputId": "0e15bd3e-d2d9-4965-df7d-c8856d036680"
-      },
-      "execution_count": null,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "(44073, 1) (2069325, 2)\n",
-            "CPU times: user 4.97 s, sys: 2.36 s, total: 7.34 s\n",
-            "Wall time: 10.6 s\n"
-          ]
+          "execution_count": 10
         }
       ]
     },
     {
-      "cell_type": "code",
+      "cell_type": "markdown",
       "source": [
-        "%%time\n",
-        "out = gg.chain([ n({'id': '116374117927631468606'}), e_forward(hops=3)])._nodes\n",
-        "out.shape"
+        "and with simple 2 and 5 hop `hop` comparison we see a 2x speedup enabled by setting g. to `cudf`"
       ],
       "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "3HJOItZ4MQMG",
-        "outputId": "f5be7bb4-7f09-4f80-c549-e703e99f5067"
-      },
-      "execution_count": null,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "CPU times: user 3min 45s, sys: 1min 5s, total: 4min 50s\n",
-            "Wall time: 4min 52s\n"
-          ]
-        },
-        {
-          "output_type": "execute_result",
-          "data": {
-            "text/plain": [
-              "(102414, 1)"
-            ]
-          },
-          "metadata": {},
-          "execution_count": 79
-        }
-      ]
+        "id": "5-7M9sPEAf5Z"
+      }
     },
     {
       "cell_type": "code",
       "source": [
-        "%%time\n",
-        "gg_gdf = gg.nodes(lambda g: cudf.DataFrame(g._nodes)).edges(lambda g: cudf.DataFrame(g._edges))\n",
-        "out = gg_gdf.chain([ n({'id': '116374117927631468606'}), e_forward(hops=3)])\n",
-        "print(out._nodes.shape, out._edges.shape)\n",
-        "del gg_gdf\n",
-        "del out"
+        "results_df = pd.DataFrame(columns=['hops', 'CPU hop time (s)', 'GPU hop time (s)', 'n_notation speedup'])\n",
+        "\n",
+        "\n",
+        "\n",
+        "for n_hop in [2,5]:\n",
+        "    start_nodes = pd.DataFrame({fg._node: [0]})\n",
+        "    start0 = time.time()\n",
+        "    for i in range(100):\n",
+        "        fg2 = fg.hop(\n",
+        "            nodes=start_nodes,\n",
+        "            direction='forward',\n",
+        "            hops=n_hop)\n",
+        "    end0 = time.time()\n",
+        "    T0 = end0-start0\n",
+        "    start_nodes = cudf.DataFrame({fg._node: [0]})\n",
+        "    fg_gdf = fg.nodes(cudf.from_pandas(fg._nodes)).edges(cudf.from_pandas(fg._edges))\n",
+        "    start1 = time.time()\n",
+        "    for i in range(100):\n",
+        "        fg2 = fg_gdf.hop(\n",
+        "            nodes=start_nodes,\n",
+        "            direction='forward',\n",
+        "            hops=n_hop)\n",
+        "    end1 = time.time()\n",
+        "\n",
+        "    del fg_gdf\n",
+        "    del fg2\n",
+        "    T1 = end1-start1\n",
+        "\n",
+        "    new_row = pd.DataFrame({\n",
+        "        'hops': [n_hop],\n",
+        "        'CPU hop time (s)': [np.round(T0, 4)],\n",
+        "        'GPU hop time (s)': [np.round(T1, 4)],\n",
+        "        'n_notation speedup': [np.round(T0 / T1, 4)]\n",
+        "    })\n",
+        "\n",
+        "    results_df = pd.concat([results_df, new_row], ignore_index=True)\n",
+        "\n",
+        "# print(results_df)"
       ],
       "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "G32t_xthOUle",
-        "outputId": "7721741f-9c86-41aa-eb0b-2c8f0db2ed54"
+        "id": "Tki_0-_j3XKG"
       },
       "execution_count": null,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "(102414, 1) (24851333, 2)\n",
-            "CPU times: user 6.95 s, sys: 2.63 s, total: 9.57 s\n",
-            "Wall time: 9.84 s\n"
-          ]
-        }
-      ]
+      "outputs": []
     },
     {
       "cell_type": "code",
       "source": [
-        "%%time\n",
-        "out = gg.chain([ n({'id': '116374117927631468606'}), e_forward(hops=4)])\n",
-        "print(out._nodes.shape, out._edges.shape)"
+        "results_df.T"
       ],
       "metadata": {
         "colab": {
-          "base_uri": "https://localhost:8080/"
+          "base_uri": "https://localhost:8080/",
+          "height": 175
         },
-        "id": "bXy2yyJsMsEG",
-        "outputId": "911f2680-067c-44f2-9ba2-7f27d3c9bc6b"
+        "id": "J_shIUugtU4D",
+        "outputId": "0877c04b-e1fc-4cdc-c928-54058ae184c8"
       },
-      "execution_count": 8,
+      "execution_count": 13,
       "outputs": [
         {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "(105479, 1) (30450354, 2)\n",
-            "CPU times: user 4min 36s, sys: 1min 25s, total: 6min 2s\n",
-            "Wall time: 6min 4s\n"
-          ]
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "                         0        1\n",
+              "hops                     2        5\n",
+              "CPU hop time (s)    5.8614  10.1756\n",
+              "GPU hop time (s)    2.3729   5.4458\n",
+              "n_notation speedup  2.4701   1.8685"
+            ],
+            "text/html": [
+              "\n",
+              "  <div id=\"df-eca34f86-0680-4ebd-8060-57a9ee0b5e05\" class=\"colab-df-container\">\n",
+              "    <div>\n",
+              "<style scoped>\n",
+              "    .dataframe tbody tr th:only-of-type {\n",
+              "        vertical-align: middle;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe tbody tr th {\n",
+              "        vertical-align: top;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe thead th {\n",
+              "        text-align: right;\n",
+              "    }\n",
+              "</style>\n",
+              "<table border=\"1\" class=\"dataframe\">\n",
+              "  <thead>\n",
+              "    <tr style=\"text-align: right;\">\n",
+              "      <th></th>\n",
+              "      <th>0</th>\n",
+              "      <th>1</th>\n",
+              "    </tr>\n",
+              "  </thead>\n",
+              "  <tbody>\n",
+              "    <tr>\n",
+              "      <th>hops</th>\n",
+              "      <td>2</td>\n",
+              "      <td>5</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>CPU hop time (s)</th>\n",
+              "      <td>5.8614</td>\n",
+              "      <td>10.1756</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>GPU hop time (s)</th>\n",
+              "      <td>2.3729</td>\n",
+              "      <td>5.4458</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>n_notation speedup</th>\n",
+              "      <td>2.4701</td>\n",
+              "      <td>1.8685</td>\n",
+              "    </tr>\n",
+              "  </tbody>\n",
+              "</table>\n",
+              "</div>\n",
+              "    <div class=\"colab-df-buttons\">\n",
+              "\n",
+              "  <div class=\"colab-df-container\">\n",
+              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-eca34f86-0680-4ebd-8060-57a9ee0b5e05')\"\n",
+              "            title=\"Convert this dataframe to an interactive table.\"\n",
+              "            style=\"display:none;\">\n",
+              "\n",
+              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
+              "    <path d=\"M120-120v-720h720v720H120Zm60-500h600v-160H180v160Zm220 220h160v-160H400v160Zm0 220h160v-160H400v160ZM180-400h160v-160H180v160Zm440 0h160v-160H620v160ZM180-180h160v-160H180v160Zm440 0h160v-160H620v160Z\"/>\n",
+              "  </svg>\n",
+              "    </button>\n",
+              "\n",
+              "  <style>\n",
+              "    .colab-df-container {\n",
+              "      display:flex;\n",
+              "      gap: 12px;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-convert {\n",
+              "      background-color: #E8F0FE;\n",
+              "      border: none;\n",
+              "      border-radius: 50%;\n",
+              "      cursor: pointer;\n",
+              "      display: none;\n",
+              "      fill: #1967D2;\n",
+              "      height: 32px;\n",
+              "      padding: 0 0 0 0;\n",
+              "      width: 32px;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-convert:hover {\n",
+              "      background-color: #E2EBFA;\n",
+              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
+              "      fill: #174EA6;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-buttons div {\n",
+              "      margin-bottom: 4px;\n",
+              "    }\n",
+              "\n",
+              "    [theme=dark] .colab-df-convert {\n",
+              "      background-color: #3B4455;\n",
+              "      fill: #D2E3FC;\n",
+              "    }\n",
+              "\n",
+              "    [theme=dark] .colab-df-convert:hover {\n",
+              "      background-color: #434B5C;\n",
+              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
+              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
+              "      fill: #FFFFFF;\n",
+              "    }\n",
+              "  </style>\n",
+              "\n",
+              "    <script>\n",
+              "      const buttonEl =\n",
+              "        document.querySelector('#df-eca34f86-0680-4ebd-8060-57a9ee0b5e05 button.colab-df-convert');\n",
+              "      buttonEl.style.display =\n",
+              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
+              "\n",
+              "      async function convertToInteractive(key) {\n",
+              "        const element = document.querySelector('#df-eca34f86-0680-4ebd-8060-57a9ee0b5e05');\n",
+              "        const dataTable =\n",
+              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
+              "                                                    [key], {});\n",
+              "        if (!dataTable) return;\n",
+              "\n",
+              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
+              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
+              "          + ' to learn more about interactive tables.';\n",
+              "        element.innerHTML = '';\n",
+              "        dataTable['output_type'] = 'display_data';\n",
+              "        await google.colab.output.renderOutput(dataTable, element);\n",
+              "        const docLink = document.createElement('div');\n",
+              "        docLink.innerHTML = docLinkHtml;\n",
+              "        element.appendChild(docLink);\n",
+              "      }\n",
+              "    </script>\n",
+              "  </div>\n",
+              "\n",
+              "\n",
+              "<div id=\"df-96074764-aa60-4100-8b70-e8194e2531eb\">\n",
+              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-96074764-aa60-4100-8b70-e8194e2531eb')\"\n",
+              "            title=\"Suggest charts\"\n",
+              "            style=\"display:none;\">\n",
+              "\n",
+              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
+              "     width=\"24px\">\n",
+              "    <g>\n",
+              "        <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
+              "    </g>\n",
+              "</svg>\n",
+              "  </button>\n",
+              "\n",
+              "<style>\n",
+              "  .colab-df-quickchart {\n",
+              "      --bg-color: #E8F0FE;\n",
+              "      --fill-color: #1967D2;\n",
+              "      --hover-bg-color: #E2EBFA;\n",
+              "      --hover-fill-color: #174EA6;\n",
+              "      --disabled-fill-color: #AAA;\n",
+              "      --disabled-bg-color: #DDD;\n",
+              "  }\n",
+              "\n",
+              "  [theme=dark] .colab-df-quickchart {\n",
+              "      --bg-color: #3B4455;\n",
+              "      --fill-color: #D2E3FC;\n",
+              "      --hover-bg-color: #434B5C;\n",
+              "      --hover-fill-color: #FFFFFF;\n",
+              "      --disabled-bg-color: #3B4455;\n",
+              "      --disabled-fill-color: #666;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart {\n",
+              "    background-color: var(--bg-color);\n",
+              "    border: none;\n",
+              "    border-radius: 50%;\n",
+              "    cursor: pointer;\n",
+              "    display: none;\n",
+              "    fill: var(--fill-color);\n",
+              "    height: 32px;\n",
+              "    padding: 0;\n",
+              "    width: 32px;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart:hover {\n",
+              "    background-color: var(--hover-bg-color);\n",
+              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
+              "    fill: var(--button-hover-fill-color);\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart-complete:disabled,\n",
+              "  .colab-df-quickchart-complete:disabled:hover {\n",
+              "    background-color: var(--disabled-bg-color);\n",
+              "    fill: var(--disabled-fill-color);\n",
+              "    box-shadow: none;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-spinner {\n",
+              "    border: 2px solid var(--fill-color);\n",
+              "    border-color: transparent;\n",
+              "    border-bottom-color: var(--fill-color);\n",
+              "    animation:\n",
+              "      spin 1s steps(1) infinite;\n",
+              "  }\n",
+              "\n",
+              "  @keyframes spin {\n",
+              "    0% {\n",
+              "      border-color: transparent;\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "      border-left-color: var(--fill-color);\n",
+              "    }\n",
+              "    20% {\n",
+              "      border-color: transparent;\n",
+              "      border-left-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "    }\n",
+              "    30% {\n",
+              "      border-color: transparent;\n",
+              "      border-left-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "      border-right-color: var(--fill-color);\n",
+              "    }\n",
+              "    40% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "    }\n",
+              "    60% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "    }\n",
+              "    80% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "    }\n",
+              "    90% {\n",
+              "      border-color: transparent;\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "    }\n",
+              "  }\n",
+              "</style>\n",
+              "\n",
+              "  <script>\n",
+              "    async function quickchart(key) {\n",
+              "      const quickchartButtonEl =\n",
+              "        document.querySelector('#' + key + ' button');\n",
+              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
+              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
+              "      try {\n",
+              "        const charts = await google.colab.kernel.invokeFunction(\n",
+              "            'suggestCharts', [key], {});\n",
+              "      } catch (error) {\n",
+              "        console.error('Error during call to suggestCharts:', error);\n",
+              "      }\n",
+              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
+              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
+              "    }\n",
+              "    (() => {\n",
+              "      let quickchartButtonEl =\n",
+              "        document.querySelector('#df-96074764-aa60-4100-8b70-e8194e2531eb button');\n",
+              "      quickchartButtonEl.style.display =\n",
+              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
+              "    })();\n",
+              "  </script>\n",
+              "</div>\n",
+              "\n",
+              "    </div>\n",
+              "  </div>\n"
+            ],
+            "application/vnd.google.colaboratory.intrinsic+json": {
+              "type": "dataframe",
+              "summary": "{\n  \"name\": \"results_df\",\n  \"rows\": 4,\n  \"fields\": [\n    {\n      \"column\": 0,\n      \"properties\": {\n        \"dtype\": \"date\",\n        \"min\": 2,\n        \"max\": 5.8614,\n        \"num_unique_values\": 4,\n        \"samples\": [\n          5.8614,\n          2.4701,\n          2\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": 1,\n      \"properties\": {\n        \"dtype\": \"date\",\n        \"min\": 1.8685,\n        \"max\": 10.1756,\n        \"num_unique_values\": 4,\n        \"samples\": [\n          10.1756,\n          1.8685,\n          5\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
+            }
+          },
+          "metadata": {},
+          "execution_count": 13
         }
       ]
     },
     {
-      "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "gg_gdf = gg.nodes(lambda g: cudf.DataFrame(g._nodes)).edges(lambda g: cudf.DataFrame(g._edges))\n",
-        "out = gg_gdf.chain([ n({'id': '116374117927631468606'}), e_forward(hops=4)])\n",
-        "print(out._nodes.shape, out._edges.shape)\n",
-        "del gg_gdf\n",
-        "del out"
-      ],
+      "cell_type": "markdown",
       "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "Vt8hhjWDP_W_",
-        "outputId": "824ae644-e1cf-4239-bda9-84aecde52ad8"
+        "id": "KrJKjXy2KLos"
       },
-      "execution_count": null,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "(105479, 1) (30450354, 2)\n",
-            "CPU times: user 7.44 s, sys: 2.45 s, total: 9.88 s\n",
-            "Wall time: 9.9 s\n"
-          ]
-        }
-      ]
-    },
-    {
-      "cell_type": "code",
       "source": [
-        "%%time\n",
-        "out = gg.chain([ n({'id': '116374117927631468606'}), e_forward(hops=5)])\n",
-        "print(out._nodes.shape, out._edges.shape)"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "_z4KpNZaOH8t",
-        "outputId": "2417f78b-e1b7-452d-8e26-7df259620c88"
-      },
-      "execution_count": 9,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "(105604, 1) (30468335, 2)\n",
-            "CPU times: user 5min 36s, sys: 1min 39s, total: 7min 16s\n",
-            "Wall time: 7min 15s\n"
-          ]
-        }
+        "<a name=\"tw\"></a>\n",
+        "## Twitter\n",
+        "\n",
+        "- edges: 2420766\n",
+        "- nodes: 81306"
       ]
     },
     {
       "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "gg_gdf = gg.nodes(lambda g: cudf.DataFrame(g._nodes)).edges(lambda g: cudf.DataFrame(g._edges))\n",
-        "out = gg_gdf.chain([ n({'id': '116374117927631468606'}), e_forward(hops=5)])\n",
-        "print(out._nodes.shape, out._edges.shape)\n",
-        "del gg_gdf\n",
-        "del out"
-      ],
+      "execution_count": 15,
       "metadata": {
-        "id": "spUBH9EHSz2O",
         "colab": {
           "base_uri": "https://localhost:8080/"
         },
-        "outputId": "22340ce3-e8d4-4a72-b485-9839c667b965"
+        "id": "fO2qasGqpubr",
+        "outputId": "63c76f29-28ef-4e6d-ff83-13365d680632"
       },
-      "execution_count": null,
       "outputs": [
         {
           "output_type": "stream",
           "name": "stdout",
           "text": [
-            "(105604, 1) (30468335, 2)\n",
-            "CPU times: user 8.82 s, sys: 2.71 s, total: 11.5 s\n",
-            "Wall time: 11.9 s\n"
+            "--2024-07-09 13:36:53--  https://snap.stanford.edu/data/twitter_combined.txt.gz\n",
+            "Resolving snap.stanford.edu (snap.stanford.edu)... 171.64.75.80\n",
+            "Connecting to snap.stanford.edu (snap.stanford.edu)|171.64.75.80|:443... connected.\n",
+            "HTTP request sent, awaiting response... 200 OK\n",
+            "Length: 10621918 (10M) [application/x-gzip]\n",
+            "Saving to: ‘twitter_combined.txt.gz’\n",
+            "\n",
+            "twitter_combined.tx 100%[===================>]  10.13M  19.6MB/s    in 0.5s    \n",
+            "\n",
+            "2024-07-09 13:36:54 (19.6 MB/s) - ‘twitter_combined.txt.gz’ saved [10621918/10621918]\n",
+            "\n"
           ]
         }
-      ]
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "start_nodes = pd.DataFrame({gg._node: ['116374117927631468606']})\n",
-        "for i in range(1):\n",
-        "  g2 = gg.hop(\n",
-        "      nodes=start_nodes,\n",
-        "      direction='forward',\n",
-        "      hops=1)\n",
-        "print(g2._nodes.shape, g2._edges.shape)"
       ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "vCsdmc62A7OM",
-        "outputId": "adc05d29-c628-49ed-cd6d-8921c6dcd206"
-      },
-      "execution_count": 50,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "(1473, 1) (13375, 2)\n",
-            "CPU times: user 19.9 s, sys: 9.36 s, total: 29.2 s\n",
-            "Wall time: 41.8 s\n"
-          ]
-        }
-      ]
-    },
-    {
-      "cell_type": "code",
       "source": [
-        "%%time\n",
-        "start_nodes = cudf.DataFrame({gg._node: ['116374117927631468606']})\n",
-        "gg_gdf = gg.nodes(cudf.from_pandas(gg._nodes)).edges(cudf.from_pandas(gg._edges))\n",
-        "for i in range(1):\n",
-        "  g2 = gg_gdf.hop(\n",
-        "      nodes=start_nodes,\n",
-        "      direction='forward',\n",
-        "      hops=1)\n",
-        "print(g2._nodes.shape, g2._edges.shape)\n",
-        "del start_nodes\n",
-        "del gg_gdf\n",
-        "del g2"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "J3kV8NBYBQdW",
-        "outputId": "76073248-43e1-4c3c-c004-67324cc1d312"
-      },
-      "execution_count": 52,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "(1473, 1) (13375, 2)\n",
-            "CPU times: user 3.71 s, sys: 2.09 s, total: 5.8 s\n",
-            "Wall time: 6.05 s\n"
-          ]
-        }
+        "! wget 'https://snap.stanford.edu/data/twitter_combined.txt.gz'\n",
+        "#! curl -L 'https://snap.stanford.edu/data/twitter_combined.txt.gz' -o twitter_combined.txt.gz"
       ]
     },
     {
       "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "start_nodes = pd.DataFrame({gg._node: ['116374117927631468606']})\n",
-        "for i in range(1):\n",
-        "  g2 = gg.hop(\n",
-        "      nodes=start_nodes,\n",
-        "      direction='forward',\n",
-        "      hops=2)\n",
-        "print(g2._nodes.shape, g2._edges.shape)"
-      ],
+      "execution_count": 16,
       "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "ONv1RQeWBeeK",
-        "outputId": "58d57fa4-be72-45bc-abfa-5de9d1102f55"
+        "id": "fn7zeA3SGlEo"
       },
-      "execution_count": 53,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "(44073, 1) (2069325, 2)\n",
-            "CPU times: user 27.8 s, sys: 13.2 s, total: 41 s\n",
-            "Wall time: 43.9 s\n"
-          ]
-        }
-      ]
-    },
-    {
-      "cell_type": "code",
+      "outputs": [],
       "source": [
-        "%%time\n",
-        "start_nodes = cudf.DataFrame({gg._node: ['116374117927631468606']})\n",
-        "gg_gdf = gg.nodes(cudf.from_pandas(gg._nodes)).edges(cudf.from_pandas(gg._edges))\n",
-        "for i in range(1):\n",
-        "  g2 = gg_gdf.hop(\n",
-        "      nodes=start_nodes,\n",
-        "      direction='forward',\n",
-        "      hops=2)\n",
-        "print(g2._nodes.shape, g2._edges.shape)\n",
-        "del start_nodes\n",
-        "del gg_gdf\n",
-        "del g2"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "ke5SZZ01BgqR",
-        "outputId": "4173fd28-a11b-4300-d28b-6fdb87e8e9f3"
-      },
-      "execution_count": 54,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "(44073, 1) (2069325, 2)\n",
-            "CPU times: user 4.26 s, sys: 2.37 s, total: 6.63 s\n",
-            "Wall time: 7.91 s\n"
-          ]
-        }
+        "! gunzip twitter_combined.txt.gz"
       ]
     },
     {
       "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "start_nodes = pd.DataFrame({gg._node: ['116374117927631468606']})\n",
-        "for i in range(1):\n",
-        "  g2 = gg.hop(\n",
-        "      nodes=start_nodes,\n",
-        "      direction='forward',\n",
-        "      hops=3)\n",
-        "print(g2._nodes.shape, g2._edges.shape)"
-      ],
+      "execution_count": 17,
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/"
         },
-        "id": "U795pIBUBiZV",
-        "outputId": "d499433c-cc0c-4bbf-c69f-36b5d55402d9"
+        "id": "68TAZkhLGz9g",
+        "outputId": "156f3da8-50c9-4e30-d1e5-9dba63e7f93d"
       },
-      "execution_count": 55,
       "outputs": [
         {
           "output_type": "stream",
           "name": "stdout",
           "text": [
-            "(102414, 1) (24851333, 2)\n",
-            "CPU times: user 1min 3s, sys: 22.7 s, total: 1min 26s\n",
-            "Wall time: 1min 35s\n"
+            "214328887 34428380\n",
+            "17116707 28465635\n",
+            "380580781 18996905\n",
+            "221036078 153460275\n",
+            "107830991 17868918\n"
           ]
         }
-      ]
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "start_nodes = cudf.DataFrame({gg._node: ['116374117927631468606']})\n",
-        "gg_gdf = gg.nodes(cudf.from_pandas(gg._nodes)).edges(cudf.from_pandas(gg._edges))\n",
-        "for i in range(1):\n",
-        "  g2 = gg_gdf.hop(\n",
-        "      nodes=start_nodes,\n",
-        "      direction='forward',\n",
-        "      hops=3)\n",
-        "print(g2._nodes.shape, g2._edges.shape)\n",
-        "del start_nodes\n",
-        "del gg_gdf\n",
-        "del g2"
       ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "kIZYwSe1Bj2e",
-        "outputId": "b7e1ed9f-47d1-412e-9593-ecc436ac1486"
-      },
-      "execution_count": 56,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "(102414, 1) (24851333, 2)\n",
-            "CPU times: user 3.96 s, sys: 2.11 s, total: 6.07 s\n",
-            "Wall time: 6.05 s\n"
-          ]
-        }
-      ]
-    },
-    {
-      "cell_type": "code",
       "source": [
-        "%%time\n",
-        "start_nodes = pd.DataFrame({gg._node: ['116374117927631468606']})\n",
-        "for i in range(1):\n",
-        "  g2 = gg.hop(\n",
-        "      nodes=start_nodes,\n",
-        "      direction='forward',\n",
-        "      hops=4)\n",
-        "print(g2._nodes.shape, g2._edges.shape)"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "YTI5sD6YBpYL",
-        "outputId": "b37bf2df-07dc-404c-8a83-a83f28e38bf6"
-      },
-      "execution_count": 57,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "(105479, 1) (30450354, 2)\n",
-            "CPU times: user 1min 34s, sys: 30.6 s, total: 2min 5s\n",
-            "Wall time: 2min 5s\n"
-          ]
-        }
+        "! head -n 5 twitter_combined.txt"
       ]
     },
     {
       "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "start_nodes = cudf.DataFrame({gg._node: ['116374117927631468606']})\n",
-        "gg_gdf = gg.nodes(cudf.from_pandas(gg._nodes)).edges(cudf.from_pandas(gg._edges))\n",
-        "for i in range(1):\n",
-        "  g2 = gg_gdf.hop(\n",
-        "      nodes=start_nodes,\n",
-        "      direction='forward',\n",
-        "      hops=4)\n",
-        "print(g2._nodes.shape, g2._edges.shape)\n",
-        "del start_nodes\n",
-        "del gg_gdf\n",
-        "del g2"
-      ],
+      "execution_count": 18,
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/"
         },
-        "id": "d5WBazICBrSz",
-        "outputId": "ef95e893-3a0f-4d47-ede4-bd8a6faebf98"
+        "id": "QU2wNeGXG2GC",
+        "outputId": "86439d2a-e85a-4e84-ee53-dfa5e0e89ce2"
       },
-      "execution_count": 58,
       "outputs": [
         {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "(105479, 1) (30450354, 2)\n",
-            "CPU times: user 5.25 s, sys: 2.41 s, total: 7.67 s\n",
-            "Wall time: 7.69 s\n"
-          ]
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "(2420766, 2)"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 18
         }
+      ],
+      "source": [
+        "te_df = pd.read_csv('twitter_combined.txt', sep=' ', names=['s', 'd'])\n",
+        "te_df.shape"
       ]
     },
     {
       "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "start_nodes = pd.DataFrame({gg._node: ['116374117927631468606']})\n",
-        "for i in range(1):\n",
-        "  g2 = gg.hop(\n",
-        "      nodes=start_nodes,\n",
-        "      direction='forward',\n",
-        "      hops=5)\n",
-        "print(g2._nodes.shape, g2._edges.shape)"
-      ],
+      "execution_count": 19,
       "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "ozQlRPaFBtPD",
-        "outputId": "4f1655c4-38fd-47f9-942d-836585e0d866"
+        "id": "EK5gQH2iG5UU"
       },
-      "execution_count": 59,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "(105604, 1) (30468335, 2)\n",
-            "CPU times: user 2min 16s, sys: 39.1 s, total: 2min 55s\n",
-            "Wall time: 2min 58s\n"
-          ]
-        }
+      "outputs": [],
+      "source": [
+        "import graphistry"
       ]
     },
     {
       "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "start_nodes = cudf.DataFrame({gg._node: ['116374117927631468606']})\n",
-        "gg_gdf = gg.nodes(cudf.from_pandas(gg._nodes)).edges(cudf.from_pandas(gg._edges))\n",
-        "for i in range(1):\n",
-        "  g2 = gg_gdf.hop(\n",
-        "      nodes=start_nodes,\n",
-        "      direction='forward',\n",
-        "      hops=5)\n",
-        "print(g2._nodes.shape, g2._edges.shape)\n",
-        "del start_nodes\n",
-        "del gg_gdf\n",
-        "del g2"
-      ],
+      "execution_count": 20,
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/"
         },
-        "id": "-ACkMG20B6HM",
-        "outputId": "f26c03a9-9f25-4f93-c7d3-0e8676694040"
+        "id": "ZtIW-eFGG_R4",
+        "outputId": "4082a078-3af9-4c4e-dc98-ddeee50a2489"
       },
-      "execution_count": 60,
       "outputs": [
         {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "(105604, 1) (30468335, 2)\n",
-            "CPU times: user 5.79 s, sys: 2.51 s, total: 8.3 s\n",
-            "Wall time: 8.29 s\n"
-          ]
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "(81306, 1)"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 20
         }
+      ],
+      "source": [
+        "g = graphistry.edges(te_df, 's', 'd').materialize_nodes()\n",
+        "g._nodes.shape"
       ]
     },
     {
       "cell_type": "markdown",
       "source": [
-        "### Orkut\n",
-        "- 117M edges\n",
-        "- 3M nodes"
+        "on the twitter data, simpler `chain` operations over several different hops -- **10-20x** *italicized text* speed increases"
       ],
       "metadata": {
-        "id": "R03M_swxarKC"
+        "id": "yR9Qr8tGww3b"
       }
     },
     {
       "cell_type": "code",
       "source": [
-        "! wget https://snap.stanford.edu/data/bigdata/communities/com-orkut.ungraph.txt.gz"
+        "results_df = pd.DataFrame(columns=['hops', 'CPU hop chain time (s)', 'GPU hop chain time (s)', 'n_notation speedup'])\n",
+        "\n",
+        "\n",
+        "for n_hop in [1,2,8]:\n",
+        "    start_nodes = pd.DataFrame({fg._node: [0]})\n",
+        "    start0 = time.time()\n",
+        "    for i in range(10):\n",
+        "        g2 = g.chain([n({'id': 17116707}), e_forward(hops=n_hop)])\n",
+        "    end0 = time.time()\n",
+        "    T0 = end0-start0\n",
+        "    g_gdf = g.nodes(lambda g: cudf.DataFrame(g._nodes)).edges(lambda g: cudf.DataFrame(g._edges))\n",
+        "    start1 = time.time()\n",
+        "    for i in range(10):\n",
+        "        out = g_gdf.chain([n({'id': 17116707}), e_forward(hops=n_hop)])._nodes\n",
+        "    end1 = time.time()\n",
+        "\n",
+        "    del g_gdf\n",
+        "    del out\n",
+        "    T1 = end1-start1\n",
+        "\n",
+        "    new_row = pd.DataFrame({\n",
+        "        'hops': [n_hop],\n",
+        "        'CPU hop chain time (s)': [np.round(T0, 4)],\n",
+        "        'GPU hop chain time (s)': [np.round(T1, 4)],\n",
+        "        'n_notation speedup': [np.round(T0 / T1, 4)]\n",
+        "    })\n",
+        "\n",
+        "\n",
+        "    results_df = pd.concat([results_df, new_row], ignore_index=True)\n",
+        "\n",
+        "results_df.T"
       ],
       "metadata": {
         "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "QoabYR2maxPo",
-        "outputId": "2bb6275d-46bb-42da-ec05-d0e5a58b1f77"
-      },
-      "execution_count": 8,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "--2023-12-26 00:55:52--  https://snap.stanford.edu/data/bigdata/communities/com-orkut.ungraph.txt.gz\n",
-            "Resolving snap.stanford.edu (snap.stanford.edu)... 171.64.75.80\n",
-            "Connecting to snap.stanford.edu (snap.stanford.edu)|171.64.75.80|:443... connected.\n",
-            "HTTP request sent, awaiting response... 200 OK\n",
-            "Length: 447251958 (427M) [application/x-gzip]\n",
-            "Saving to: ‘com-orkut.ungraph.txt.gz’\n",
-            "\n",
-            "com-orkut.ungraph.t 100%[===================>] 426.53M  45.1MB/s    in 9.7s    \n",
-            "\n",
-            "2023-12-26 00:56:02 (44.0 MB/s) - ‘com-orkut.ungraph.txt.gz’ saved [447251958/447251958]\n",
-            "\n"
-          ]
+          "base_uri": "https://localhost:8080/",
+          "height": 175
+        },
+        "id": "rCsvQJa-6U0x",
+        "outputId": "a8d52e0a-cd32-436d-a889-c997c6289055"
+      },
+      "execution_count": 21,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "                              0        1        2\n",
+              "hops                          1        2        8\n",
+              "CPU hop chain time (s)  19.3802    17.21  84.5977\n",
+              "GPU hop chain time (s)   0.7395   1.5332   4.4011\n",
+              "n_notation speedup      26.2058  11.2246  19.2218"
+            ],
+            "text/html": [
+              "\n",
+              "  <div id=\"df-21d18435-c815-4615-b12b-33bdfb1e5486\" class=\"colab-df-container\">\n",
+              "    <div>\n",
+              "<style scoped>\n",
+              "    .dataframe tbody tr th:only-of-type {\n",
+              "        vertical-align: middle;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe tbody tr th {\n",
+              "        vertical-align: top;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe thead th {\n",
+              "        text-align: right;\n",
+              "    }\n",
+              "</style>\n",
+              "<table border=\"1\" class=\"dataframe\">\n",
+              "  <thead>\n",
+              "    <tr style=\"text-align: right;\">\n",
+              "      <th></th>\n",
+              "      <th>0</th>\n",
+              "      <th>1</th>\n",
+              "      <th>2</th>\n",
+              "    </tr>\n",
+              "  </thead>\n",
+              "  <tbody>\n",
+              "    <tr>\n",
+              "      <th>hops</th>\n",
+              "      <td>1</td>\n",
+              "      <td>2</td>\n",
+              "      <td>8</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>CPU hop chain time (s)</th>\n",
+              "      <td>19.3802</td>\n",
+              "      <td>17.21</td>\n",
+              "      <td>84.5977</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>GPU hop chain time (s)</th>\n",
+              "      <td>0.7395</td>\n",
+              "      <td>1.5332</td>\n",
+              "      <td>4.4011</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>n_notation speedup</th>\n",
+              "      <td>26.2058</td>\n",
+              "      <td>11.2246</td>\n",
+              "      <td>19.2218</td>\n",
+              "    </tr>\n",
+              "  </tbody>\n",
+              "</table>\n",
+              "</div>\n",
+              "    <div class=\"colab-df-buttons\">\n",
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+              "  </svg>\n",
+              "    </button>\n",
+              "\n",
+              "  <style>\n",
+              "    .colab-df-container {\n",
+              "      display:flex;\n",
+              "      gap: 12px;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-convert {\n",
+              "      background-color: #E8F0FE;\n",
+              "      border: none;\n",
+              "      border-radius: 50%;\n",
+              "      cursor: pointer;\n",
+              "      display: none;\n",
+              "      fill: #1967D2;\n",
+              "      height: 32px;\n",
+              "      padding: 0 0 0 0;\n",
+              "      width: 32px;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-convert:hover {\n",
+              "      background-color: #E2EBFA;\n",
+              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
+              "      fill: #174EA6;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-buttons div {\n",
+              "      margin-bottom: 4px;\n",
+              "    }\n",
+              "\n",
+              "    [theme=dark] .colab-df-convert {\n",
+              "      background-color: #3B4455;\n",
+              "      fill: #D2E3FC;\n",
+              "    }\n",
+              "\n",
+              "    [theme=dark] .colab-df-convert:hover {\n",
+              "      background-color: #434B5C;\n",
+              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
+              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
+              "      fill: #FFFFFF;\n",
+              "    }\n",
+              "  </style>\n",
+              "\n",
+              "    <script>\n",
+              "      const buttonEl =\n",
+              "        document.querySelector('#df-21d18435-c815-4615-b12b-33bdfb1e5486 button.colab-df-convert');\n",
+              "      buttonEl.style.display =\n",
+              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
+              "\n",
+              "      async function convertToInteractive(key) {\n",
+              "        const element = document.querySelector('#df-21d18435-c815-4615-b12b-33bdfb1e5486');\n",
+              "        const dataTable =\n",
+              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
+              "                                                    [key], {});\n",
+              "        if (!dataTable) return;\n",
+              "\n",
+              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
+              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
+              "          + ' to learn more about interactive tables.';\n",
+              "        element.innerHTML = '';\n",
+              "        dataTable['output_type'] = 'display_data';\n",
+              "        await google.colab.output.renderOutput(dataTable, element);\n",
+              "        const docLink = document.createElement('div');\n",
+              "        docLink.innerHTML = docLinkHtml;\n",
+              "        element.appendChild(docLink);\n",
+              "      }\n",
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+              "\n",
+              "\n",
+              "<div id=\"df-0b9c7e11-367c-4aa6-9fdd-25705ad6086b\">\n",
+              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-0b9c7e11-367c-4aa6-9fdd-25705ad6086b')\"\n",
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+              "            style=\"display:none;\">\n",
+              "\n",
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+              "    </g>\n",
+              "</svg>\n",
+              "  </button>\n",
+              "\n",
+              "<style>\n",
+              "  .colab-df-quickchart {\n",
+              "      --bg-color: #E8F0FE;\n",
+              "      --fill-color: #1967D2;\n",
+              "      --hover-bg-color: #E2EBFA;\n",
+              "      --hover-fill-color: #174EA6;\n",
+              "      --disabled-fill-color: #AAA;\n",
+              "      --disabled-bg-color: #DDD;\n",
+              "  }\n",
+              "\n",
+              "  [theme=dark] .colab-df-quickchart {\n",
+              "      --bg-color: #3B4455;\n",
+              "      --fill-color: #D2E3FC;\n",
+              "      --hover-bg-color: #434B5C;\n",
+              "      --hover-fill-color: #FFFFFF;\n",
+              "      --disabled-bg-color: #3B4455;\n",
+              "      --disabled-fill-color: #666;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart {\n",
+              "    background-color: var(--bg-color);\n",
+              "    border: none;\n",
+              "    border-radius: 50%;\n",
+              "    cursor: pointer;\n",
+              "    display: none;\n",
+              "    fill: var(--fill-color);\n",
+              "    height: 32px;\n",
+              "    padding: 0;\n",
+              "    width: 32px;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart:hover {\n",
+              "    background-color: var(--hover-bg-color);\n",
+              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
+              "    fill: var(--button-hover-fill-color);\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart-complete:disabled,\n",
+              "  .colab-df-quickchart-complete:disabled:hover {\n",
+              "    background-color: var(--disabled-bg-color);\n",
+              "    fill: var(--disabled-fill-color);\n",
+              "    box-shadow: none;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-spinner {\n",
+              "    border: 2px solid var(--fill-color);\n",
+              "    border-color: transparent;\n",
+              "    border-bottom-color: var(--fill-color);\n",
+              "    animation:\n",
+              "      spin 1s steps(1) infinite;\n",
+              "  }\n",
+              "\n",
+              "  @keyframes spin {\n",
+              "    0% {\n",
+              "      border-color: transparent;\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "      border-left-color: var(--fill-color);\n",
+              "    }\n",
+              "    20% {\n",
+              "      border-color: transparent;\n",
+              "      border-left-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "    }\n",
+              "    30% {\n",
+              "      border-color: transparent;\n",
+              "      border-left-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "      border-right-color: var(--fill-color);\n",
+              "    }\n",
+              "    40% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "    }\n",
+              "    60% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "    }\n",
+              "    80% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "    }\n",
+              "    90% {\n",
+              "      border-color: transparent;\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "    }\n",
+              "  }\n",
+              "</style>\n",
+              "\n",
+              "  <script>\n",
+              "    async function quickchart(key) {\n",
+              "      const quickchartButtonEl =\n",
+              "        document.querySelector('#' + key + ' button');\n",
+              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
+              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
+              "      try {\n",
+              "        const charts = await google.colab.kernel.invokeFunction(\n",
+              "            'suggestCharts', [key], {});\n",
+              "      } catch (error) {\n",
+              "        console.error('Error during call to suggestCharts:', error);\n",
+              "      }\n",
+              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
+              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
+              "    }\n",
+              "    (() => {\n",
+              "      let quickchartButtonEl =\n",
+              "        document.querySelector('#df-0b9c7e11-367c-4aa6-9fdd-25705ad6086b button');\n",
+              "      quickchartButtonEl.style.display =\n",
+              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
+              "    })();\n",
+              "  </script>\n",
+              "</div>\n",
+              "\n",
+              "    </div>\n",
+              "  </div>\n"
+            ],
+            "application/vnd.google.colaboratory.intrinsic+json": {
+              "type": "dataframe",
+              "summary": "{\n  \"name\": \"results_df\",\n  \"rows\": 4,\n  \"fields\": [\n    {\n      \"column\": 0,\n      \"properties\": {\n        \"dtype\": \"date\",\n        \"min\": 0.7395,\n        \"max\": 26.2058,\n        \"num_unique_values\": 4,\n        \"samples\": [\n          19.3802,\n          26.2058,\n          1\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": 1,\n      \"properties\": {\n        \"dtype\": \"date\",\n        \"min\": 1.5332,\n        \"max\": 17.21,\n        \"num_unique_values\": 4,\n        \"samples\": [\n          17.21,\n          11.2246,\n          2\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": 2,\n      \"properties\": {\n        \"dtype\": \"date\",\n        \"min\": 4.4011,\n        \"max\": 84.5977,\n        \"num_unique_values\": 4,\n        \"samples\": [\n          84.5977,\n          19.2218,\n          8\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
+            }
+          },
+          "metadata": {},
+          "execution_count": 21
         }
       ]
     },
     {
-      "cell_type": "code",
+      "cell_type": "markdown",
       "source": [
-        "! gunzip com-orkut.ungraph.txt.gz"
+        "and similarly for these `hop` operations -- **10-30x** speed increases"
       ],
       "metadata": {
-        "id": "BvvfFPKWbAVJ"
-      },
-      "execution_count": 9,
-      "outputs": []
+        "id": "gHHhyYlzArjw"
+      }
     },
     {
-      "cell_type": "code",
-      "source": [
-        "! head -n 7 com-orkut.ungraph.txt"
-      ],
+      "cell_type": "markdown",
       "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "YsWwRoPqbPIb",
-        "outputId": "2eb4f862-b4e1-42bf-ff5d-eec10b27cedc"
+        "id": "9dZzAAVONCD2"
       },
-      "execution_count": 10,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "# Undirected graph: ../../data/output/orkut.txt\n",
-            "# Orkut\n",
-            "# Nodes: 3072441 Edges: 117185083\n",
-            "# FromNodeId\tToNodeId\n",
-            "1\t2\n",
-            "1\t3\n",
-            "1\t4\n"
-          ]
-        }
+      "source": [
+        "<a name=\"gpl\"></a>\n",
+        "## GPlus\n",
+        "\n",
+        "- edges: 30494866\n",
+        "- nodes: 107614"
       ]
     },
     {
       "cell_type": "code",
       "source": [
-        "import pandas as pd\n",
-        "\n",
-        "import graphistry\n",
+        "results_df = pd.DataFrame(columns=['hops', 'CPU hop chain time (s)', 'GPU hop chain time (s)', 'n_notation speedup'])\n",
         "\n",
-        "from graphistry import (\n",
         "\n",
-        "    # graph operators\n",
-        "    n, e_undirected, e_forward, e_reverse,\n",
+        "for n_hop in [1,2,8]:\n",
+        "    start_nodes = pd.DataFrame({g._node: [17116707]})\n",
+        "    start0 = time.time()\n",
+        "    for i in range(10):\n",
+        "      g2 = g.hop(\n",
+        "          nodes=start_nodes,\n",
+        "          direction='forward',\n",
+        "          hops=n_hop)\n",
+        "    end0 = time.time()\n",
+        "    T0 = end0-start0\n",
+        "    start_nodes = cudf.DataFrame({g._node: [17116707]})\n",
+        "    g_gdf = g.nodes(cudf.from_pandas(g._nodes)).edges(cudf.from_pandas(g._edges))\n",
+        "    start1 = time.time()\n",
+        "    for i in range(10):\n",
+        "        g2 = g_gdf.hop(\n",
+        "            nodes=start_nodes,\n",
+        "            direction='forward',\n",
+        "            hops=5)\n",
+        "    end1 = time.time()\n",
         "\n",
-        "    # attribute predicates\n",
-        "    is_in, ge, startswith, contains, match as match_re\n",
-        ")\n",
+        "    del start_nodes\n",
+        "    del g_gdf\n",
+        "    del g2\n",
+        "    T1 = end1-start1\n",
         "\n",
-        "import cudf\n",
+        "    new_row = pd.DataFrame({\n",
+        "        'hops': [n_hop],\n",
+        "        'CPU hop chain time (s)': [np.round(T0, 4)],\n",
+        "        'GPU hop chain time (s)': [np.round(T1, 4)],\n",
+        "        'n_notation speedup': [np.round(T0 / T1, 4)]\n",
+        "    })\n",
         "\n",
-        "#work around google colab shell encoding bugs\n",
-        "import locale\n",
-        "locale.getpreferredencoding = lambda: \"UTF-8\"\n",
+        "    results_df = pd.concat([results_df, new_row], ignore_index=True)\n",
         "\n",
-        "cudf.__version__, graphistry.__version__"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "cbMC8r2ldjbW",
-        "outputId": "82688d53-7d56-4563-d65e-7c5cd32ac14e"
-      },
-      "execution_count": 11,
-      "outputs": [
-        {
-          "output_type": "execute_result",
-          "data": {
-            "text/plain": [
-              "('23.12.01', '0.32.0+12.g72e778c')"
-            ]
-          },
-          "metadata": {},
-          "execution_count": 11
-        }
-      ]
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "! nvidia-smi"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "TopFxAvnh_Cv",
-        "outputId": "cc9d9dc9-e594-4190-fe84-3f1b6dce8a1a"
-      },
-      "execution_count": 12,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "Tue Dec 26 00:56:27 2023       \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| NVIDIA-SMI 535.104.05             Driver Version: 535.104.05   CUDA Version: 12.2     |\n",
-            "|-----------------------------------------+----------------------+----------------------+\n",
-            "| GPU  Name                 Persistence-M | Bus-Id        Disp.A | Volatile Uncorr. ECC |\n",
-            "| Fan  Temp   Perf          Pwr:Usage/Cap |         Memory-Usage | GPU-Util  Compute M. |\n",
-            "|                                         |                      |               MIG M. |\n",
-            "|=========================================+======================+======================|\n",
-            "|   0  Tesla T4                       Off | 00000000:00:04.0 Off |                    0 |\n",
-            "| N/A   47C    P0              27W /  70W |    103MiB / 15360MiB |      0%      Default |\n",
-            "|                                         |                      |                  N/A |\n",
-            "+-----------------------------------------+----------------------+----------------------+\n",
-            "                                                                                         \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| Processes:                                                                            |\n",
-            "|  GPU   GI   CI        PID   Type   Process name                            GPU Memory |\n",
-            "|        ID   ID                                                             Usage      |\n",
-            "|=======================================================================================|\n",
-            "+---------------------------------------------------------------------------------------+\n"
-          ]
-        }
-      ]
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "co_df = cudf.read_csv('com-orkut.ungraph.txt', sep='\\t', names=['s', 'd'], skiprows=5).to_pandas()\n",
-        "print(co_df.shape)\n",
-        "print(co_df.head(5))\n",
-        "print(co_df.dtypes)\n",
-        "#del co_df"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "Oczs87ITbJgw",
-        "outputId": "ac203ddd-e684-4eb9-a586-f6a49fd1625d"
-      },
-      "execution_count": 13,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "(117185082, 2)\n",
-            "   s  d\n",
-            "0  1  3\n",
-            "1  1  4\n",
-            "2  1  5\n",
-            "3  1  6\n",
-            "4  1  7\n",
-            "s    int64\n",
-            "d    int64\n",
-            "dtype: object\n",
-            "CPU times: user 2.56 s, sys: 4.2 s, total: 6.76 s\n",
-            "Wall time: 6.76 s\n"
-          ]
-        }
-      ]
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "co_g = graphistry.edges(cudf.DataFrame(co_df), 's', 'd').materialize_nodes(engine='cudf')\n",
-        "co_g = co_g.nodes(lambda g: g._nodes.to_pandas()).edges(lambda g: g._edges.to_pandas())\n",
-        "print(co_g._nodes.shape, co_g._edges.shape)\n",
-        "co_g._nodes.head(5)"
+        "(results_df.T)"
       ],
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/",
-          "height": 258
+          "height": 175
         },
-        "id": "gGSDjTtveFAT",
-        "outputId": "e7b38f4f-dc07-4f35-9bab-9c80a80bbf0b"
+        "id": "cnILbPnG7tf4",
+        "outputId": "3d2e0ca7-8b07-45ab-e020-222197639dc6"
       },
-      "execution_count": 14,
+      "execution_count": 22,
       "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "(3072441, 1) (117185082, 2)\n",
-            "CPU times: user 1.96 s, sys: 2.95 s, total: 4.91 s\n",
-            "Wall time: 4.92 s\n"
-          ]
-        },
         {
           "output_type": "execute_result",
           "data": {
             "text/plain": [
-              "   id\n",
-              "0   1\n",
-              "1   2\n",
-              "2   3\n",
-              "3   4\n",
-              "4   5"
+              "                              0        1        2\n",
+              "hops                          1        2        8\n",
+              "CPU hop chain time (s)  18.8525  12.5991    43.39\n",
+              "GPU hop chain time (s)   1.0538   1.0413   1.4334\n",
+              "n_notation speedup      17.8901  12.0998  30.2698"
             ],
             "text/html": [
               "\n",
-              "  <div id=\"df-a4040d48-f85c-42f4-ab06-9114b9f80264\" class=\"colab-df-container\">\n",
+              "  <div id=\"df-251dfd06-e6e8-4827-8680-a4c8b91efa05\" class=\"colab-df-container\">\n",
               "    <div>\n",
               "<style scoped>\n",
               "    .dataframe tbody tr th:only-of-type {\n",
@@ -3525,29 +2203,35 @@
               "  <thead>\n",
               "    <tr style=\"text-align: right;\">\n",
               "      <th></th>\n",
-              "      <th>id</th>\n",
+              "      <th>0</th>\n",
+              "      <th>1</th>\n",
+              "      <th>2</th>\n",
               "    </tr>\n",
               "  </thead>\n",
               "  <tbody>\n",
               "    <tr>\n",
-              "      <th>0</th>\n",
+              "      <th>hops</th>\n",
               "      <td>1</td>\n",
-              "    </tr>\n",
-              "    <tr>\n",
-              "      <th>1</th>\n",
               "      <td>2</td>\n",
+              "      <td>8</td>\n",
               "    </tr>\n",
               "    <tr>\n",
-              "      <th>2</th>\n",
-              "      <td>3</td>\n",
+              "      <th>CPU hop chain time (s)</th>\n",
+              "      <td>18.8525</td>\n",
+              "      <td>12.5991</td>\n",
+              "      <td>43.39</td>\n",
               "    </tr>\n",
               "    <tr>\n",
-              "      <th>3</th>\n",
-              "      <td>4</td>\n",
+              "      <th>GPU hop chain time (s)</th>\n",
+              "      <td>1.0538</td>\n",
+              "      <td>1.0413</td>\n",
+              "      <td>1.4334</td>\n",
               "    </tr>\n",
               "    <tr>\n",
-              "      <th>4</th>\n",
-              "      <td>5</td>\n",
+              "      <th>n_notation speedup</th>\n",
+              "      <td>17.8901</td>\n",
+              "      <td>12.0998</td>\n",
+              "      <td>30.2698</td>\n",
               "    </tr>\n",
               "  </tbody>\n",
               "</table>\n",
@@ -3555,7 +2239,7 @@
               "    <div class=\"colab-df-buttons\">\n",
               "\n",
               "  <div class=\"colab-df-container\">\n",
-              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-a4040d48-f85c-42f4-ab06-9114b9f80264')\"\n",
+              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-251dfd06-e6e8-4827-8680-a4c8b91efa05')\"\n",
               "            title=\"Convert this dataframe to an interactive table.\"\n",
               "            style=\"display:none;\">\n",
               "\n",
@@ -3607,12 +2291,12 @@
               "\n",
               "    <script>\n",
               "      const buttonEl =\n",
-              "        document.querySelector('#df-a4040d48-f85c-42f4-ab06-9114b9f80264 button.colab-df-convert');\n",
+              "        document.querySelector('#df-251dfd06-e6e8-4827-8680-a4c8b91efa05 button.colab-df-convert');\n",
               "      buttonEl.style.display =\n",
               "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
               "\n",
               "      async function convertToInteractive(key) {\n",
-              "        const element = document.querySelector('#df-a4040d48-f85c-42f4-ab06-9114b9f80264');\n",
+              "        const element = document.querySelector('#df-251dfd06-e6e8-4827-8680-a4c8b91efa05');\n",
               "        const dataTable =\n",
               "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
               "                                                    [key], {});\n",
@@ -3632,8 +2316,8 @@
               "  </div>\n",
               "\n",
               "\n",
-              "<div id=\"df-39f20af4-a46e-49ab-8703-96d31e61ff88\">\n",
-              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-39f20af4-a46e-49ab-8703-96d31e61ff88')\"\n",
+              "<div id=\"df-8e80e718-2f69-49f7-8aee-efcf76425a01\">\n",
+              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-8e80e718-2f69-49f7-8aee-efcf76425a01')\"\n",
               "            title=\"Suggest charts\"\n",
               "            style=\"display:none;\">\n",
               "\n",
@@ -3752,1074 +2436,1561 @@
               "    }\n",
               "    (() => {\n",
               "      let quickchartButtonEl =\n",
-              "        document.querySelector('#df-39f20af4-a46e-49ab-8703-96d31e61ff88 button');\n",
+              "        document.querySelector('#df-8e80e718-2f69-49f7-8aee-efcf76425a01 button');\n",
               "      quickchartButtonEl.style.display =\n",
-              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
-              "    })();\n",
-              "  </script>\n",
-              "</div>\n",
-              "    </div>\n",
-              "  </div>\n"
-            ]
-          },
-          "metadata": {},
-          "execution_count": 14
-        }
-      ]
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "! nvidia-smi"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "V5qL8K7-dqIZ",
-        "outputId": "e08319fc-74d3-4f33-df0f-f98950dc8c99"
-      },
-      "execution_count": 15,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "Tue Dec 26 00:56:39 2023       \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| NVIDIA-SMI 535.104.05             Driver Version: 535.104.05   CUDA Version: 12.2     |\n",
-            "|-----------------------------------------+----------------------+----------------------+\n",
-            "| GPU  Name                 Persistence-M | Bus-Id        Disp.A | Volatile Uncorr. ECC |\n",
-            "| Fan  Temp   Perf          Pwr:Usage/Cap |         Memory-Usage | GPU-Util  Compute M. |\n",
-            "|                                         |                      |               MIG M. |\n",
-            "|=========================================+======================+======================|\n",
-            "|   0  Tesla T4                       Off | 00000000:00:04.0 Off |                    0 |\n",
-            "| N/A   49C    P0              27W /  70W |   2819MiB / 15360MiB |      0%      Default |\n",
-            "|                                         |                      |                  N/A |\n",
-            "+-----------------------------------------+----------------------+----------------------+\n",
-            "                                                                                         \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| Processes:                                                                            |\n",
-            "|  GPU   GI   CI        PID   Type   Process name                            GPU Memory |\n",
-            "|        ID   ID                                                             Usage      |\n",
-            "|=======================================================================================|\n",
-            "+---------------------------------------------------------------------------------------+\n"
-          ]
-        }
-      ]
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "# crashes\n",
-        "if False:\n",
-        "  out = co_g.chain([ n({'id': 1}), e_forward(hops=1)])._nodes\n",
-        "  print(out.shape)\n",
-        "  del out"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "hCbxZ8UmhRLp",
-        "outputId": "519aed6c-733d-41f4-d462-e57f5e32b131"
-      },
-      "execution_count": null,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "CPU times: user 4 µs, sys: 1 µs, total: 5 µs\n",
-            "Wall time: 47.7 µs\n"
-          ]
-        }
-      ]
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "co_gdf = co_g.nodes(lambda g: cudf.DataFrame(g._nodes)).edges(lambda g: cudf.DataFrame(g._edges))\n",
-        "! nvidia-smi\n",
-        "for i in range(10):\n",
-        "  out = co_gdf.chain([ n({'id': 1}), e_forward(hops=1)])\n",
-        "! nvidia-smi\n",
-        "print(out._nodes.shape, out._edges.shape)\n",
-        "del co_gdf\n",
-        "del out"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "Q682scC_eC-S",
-        "outputId": "7ff5f829-0de7-4a6c-a77d-e2857896a8a5"
-      },
-      "execution_count": null,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "Mon Dec 25 06:23:46 2023       \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| NVIDIA-SMI 535.104.05             Driver Version: 535.104.05   CUDA Version: 12.2     |\n",
-            "|-----------------------------------------+----------------------+----------------------+\n",
-            "| GPU  Name                 Persistence-M | Bus-Id        Disp.A | Volatile Uncorr. ECC |\n",
-            "| Fan  Temp   Perf          Pwr:Usage/Cap |         Memory-Usage | GPU-Util  Compute M. |\n",
-            "|                                         |                      |               MIG M. |\n",
-            "|=========================================+======================+======================|\n",
-            "|   0  Tesla T4                       Off | 00000000:00:04.0 Off |                    0 |\n",
-            "| N/A   63C    P0              30W /  70W |   1925MiB / 15360MiB |     35%      Default |\n",
-            "|                                         |                      |                  N/A |\n",
-            "+-----------------------------------------+----------------------+----------------------+\n",
-            "                                                                                         \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| Processes:                                                                            |\n",
-            "|  GPU   GI   CI        PID   Type   Process name                            GPU Memory |\n",
-            "|        ID   ID                                                             Usage      |\n",
-            "|=======================================================================================|\n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "Mon Dec 25 06:23:49 2023       \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| NVIDIA-SMI 535.104.05             Driver Version: 535.104.05   CUDA Version: 12.2     |\n",
-            "|-----------------------------------------+----------------------+----------------------+\n",
-            "| GPU  Name                 Persistence-M | Bus-Id        Disp.A | Volatile Uncorr. ECC |\n",
-            "| Fan  Temp   Perf          Pwr:Usage/Cap |         Memory-Usage | GPU-Util  Compute M. |\n",
-            "|                                         |                      |               MIG M. |\n",
-            "|=========================================+======================+======================|\n",
-            "|   0  Tesla T4                       Off | 00000000:00:04.0 Off |                    0 |\n",
-            "| N/A   66C    P0              72W /  70W |   2845MiB / 15360MiB |     84%      Default |\n",
-            "|                                         |                      |                  N/A |\n",
-            "+-----------------------------------------+----------------------+----------------------+\n",
-            "                                                                                         \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| Processes:                                                                            |\n",
-            "|  GPU   GI   CI        PID   Type   Process name                            GPU Memory |\n",
-            "|        ID   ID                                                             Usage      |\n",
-            "|=======================================================================================|\n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "(12, 1) (11, 2)\n",
-            "CPU times: user 4.42 s, sys: 131 ms, total: 4.55 s\n",
-            "Wall time: 4.42 s\n"
-          ]
+              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
+              "    })();\n",
+              "  </script>\n",
+              "</div>\n",
+              "\n",
+              "    </div>\n",
+              "  </div>\n"
+            ],
+            "application/vnd.google.colaboratory.intrinsic+json": {
+              "type": "dataframe",
+              "summary": "{\n  \"name\": \"(results_df\",\n  \"rows\": 4,\n  \"fields\": [\n    {\n      \"column\": 0,\n      \"properties\": {\n        \"dtype\": \"date\",\n        \"min\": 1,\n        \"max\": 18.8525,\n        \"num_unique_values\": 4,\n        \"samples\": [\n          18.8525,\n          17.8901,\n          1\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": 1,\n      \"properties\": {\n        \"dtype\": \"date\",\n        \"min\": 1.0413,\n        \"max\": 12.5991,\n        \"num_unique_values\": 4,\n        \"samples\": [\n          12.5991,\n          12.0998,\n          2\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": 2,\n      \"properties\": {\n        \"dtype\": \"date\",\n        \"min\": 1.4334,\n        \"max\": 43.39,\n        \"num_unique_values\": 4,\n        \"samples\": [\n          43.39,\n          30.2698,\n          8\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
+            }
+          },
+          "metadata": {},
+          "execution_count": 22
         }
       ]
     },
     {
       "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "co_gdf = co_g.nodes(lambda g: cudf.DataFrame(g._nodes)).edges(lambda g: cudf.DataFrame(g._edges))\n",
-        "! nvidia-smi\n",
-        "for i in range(10):\n",
-        "  out = co_gdf.chain([ n({'id': 1}), e_forward(hops=2)])\n",
-        "! nvidia-smi\n",
-        "print(out._nodes.shape, out._edges.shape)\n",
-        "del co_gdf\n",
-        "del out"
-      ],
+      "execution_count": 23,
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/"
         },
-        "id": "i0AXhfqVbVsm",
-        "outputId": "8271f469-a73f-48e3-e1a9-3077026ab8ec"
+        "id": "-nhWGNekKpcZ",
+        "outputId": "089265f4-157b-471a-c590-047fb670b47e"
       },
-      "execution_count": null,
       "outputs": [
         {
           "output_type": "stream",
           "name": "stdout",
           "text": [
-            "Mon Dec 25 06:24:52 2023       \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| NVIDIA-SMI 535.104.05             Driver Version: 535.104.05   CUDA Version: 12.2     |\n",
-            "|-----------------------------------------+----------------------+----------------------+\n",
-            "| GPU  Name                 Persistence-M | Bus-Id        Disp.A | Volatile Uncorr. ECC |\n",
-            "| Fan  Temp   Perf          Pwr:Usage/Cap |         Memory-Usage | GPU-Util  Compute M. |\n",
-            "|                                         |                      |               MIG M. |\n",
-            "|=========================================+======================+======================|\n",
-            "|   0  Tesla T4                       Off | 00000000:00:04.0 Off |                    0 |\n",
-            "| N/A   61C    P0              29W /  70W |   1925MiB / 15360MiB |     22%      Default |\n",
-            "|                                         |                      |                  N/A |\n",
-            "+-----------------------------------------+----------------------+----------------------+\n",
-            "                                                                                         \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| Processes:                                                                            |\n",
-            "|  GPU   GI   CI        PID   Type   Process name                            GPU Memory |\n",
-            "|        ID   ID                                                             Usage      |\n",
-            "|=======================================================================================|\n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "Mon Dec 25 06:24:58 2023       \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| NVIDIA-SMI 535.104.05             Driver Version: 535.104.05   CUDA Version: 12.2     |\n",
-            "|-----------------------------------------+----------------------+----------------------+\n",
-            "| GPU  Name                 Persistence-M | Bus-Id        Disp.A | Volatile Uncorr. ECC |\n",
-            "| Fan  Temp   Perf          Pwr:Usage/Cap |         Memory-Usage | GPU-Util  Compute M. |\n",
-            "|                                         |                      |               MIG M. |\n",
-            "|=========================================+======================+======================|\n",
-            "|   0  Tesla T4                       Off | 00000000:00:04.0 Off |                    0 |\n",
-            "| N/A   64C    P0              71W /  70W |   2845MiB / 15360MiB |     57%      Default |\n",
-            "|                                         |                      |                  N/A |\n",
-            "+-----------------------------------------+----------------------+----------------------+\n",
-            "                                                                                         \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| Processes:                                                                            |\n",
-            "|  GPU   GI   CI        PID   Type   Process name                            GPU Memory |\n",
-            "|        ID   ID                                                             Usage      |\n",
-            "|=======================================================================================|\n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "(391, 1) (461, 2)\n",
-            "CPU times: user 5.34 s, sys: 132 ms, total: 5.47 s\n",
-            "Wall time: 6.13 s\n"
+            "--2024-07-09 13:41:10--  https://snap.stanford.edu/data/gplus_combined.txt.gz\n",
+            "Resolving snap.stanford.edu (snap.stanford.edu)... 171.64.75.80\n",
+            "Connecting to snap.stanford.edu (snap.stanford.edu)|171.64.75.80|:443... connected.\n",
+            "HTTP request sent, awaiting response... 200 OK\n",
+            "Length: 398930514 (380M) [application/x-gzip]\n",
+            "Saving to: ‘gplus_combined.txt.gz’\n",
+            "\n",
+            "gplus_combined.txt. 100%[===================>] 380.45M  39.1MB/s    in 9.6s    \n",
+            "\n",
+            "2024-07-09 13:41:19 (39.7 MB/s) - ‘gplus_combined.txt.gz’ saved [398930514/398930514]\n",
+            "\n"
           ]
         }
+      ],
+      "source": [
+        "! wget https://snap.stanford.edu/data/gplus_combined.txt.gz"
       ]
     },
     {
       "cell_type": "code",
+      "execution_count": 24,
+      "metadata": {
+        "id": "g5wgA_c2KqwJ"
+      },
+      "outputs": [],
       "source": [
-        "%%time\n",
-        "co_gdf = co_g.nodes(lambda g: cudf.DataFrame(g._nodes)).edges(lambda g: cudf.DataFrame(g._edges))\n",
-        "! nvidia-smi\n",
-        "for i in range(10):\n",
-        "  out = co_gdf.chain([ n({'id': 1}), e_forward(hops=3)])\n",
-        "! nvidia-smi\n",
-        "print(out._nodes.shape, out._edges.shape)\n",
-        "del co_gdf\n",
-        "del out"
-      ],
+        "! gunzip gplus_combined.txt.gz"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 25,
       "metadata": {
+        "id": "52hgDbr0Kti6",
         "colab": {
-          "base_uri": "https://localhost:8080/"
+          "base_uri": "https://localhost:8080/",
+          "height": 260
         },
-        "id": "Hid0-iPKhpOd",
-        "outputId": "ecaeb534-d4d7-48fa-d4e1-c80b22626afe"
+        "outputId": "75c5a7c1-43fa-4f5b-bc92-f9ce6812bea2"
       },
-      "execution_count": null,
       "outputs": [
         {
           "output_type": "stream",
           "name": "stdout",
           "text": [
-            "Mon Dec 25 06:25:25 2023       \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| NVIDIA-SMI 535.104.05             Driver Version: 535.104.05   CUDA Version: 12.2     |\n",
-            "|-----------------------------------------+----------------------+----------------------+\n",
-            "| GPU  Name                 Persistence-M | Bus-Id        Disp.A | Volatile Uncorr. ECC |\n",
-            "| Fan  Temp   Perf          Pwr:Usage/Cap |         Memory-Usage | GPU-Util  Compute M. |\n",
-            "|                                         |                      |               MIG M. |\n",
-            "|=========================================+======================+======================|\n",
-            "|   0  Tesla T4                       Off | 00000000:00:04.0 Off |                    0 |\n",
-            "| N/A   61C    P0              29W /  70W |   1925MiB / 15360MiB |     31%      Default |\n",
-            "|                                         |                      |                  N/A |\n",
-            "+-----------------------------------------+----------------------+----------------------+\n",
-            "                                                                                         \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| Processes:                                                                            |\n",
-            "|  GPU   GI   CI        PID   Type   Process name                            GPU Memory |\n",
-            "|        ID   ID                                                             Usage      |\n",
-            "|=======================================================================================|\n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "Mon Dec 25 06:25:31 2023       \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| NVIDIA-SMI 535.104.05             Driver Version: 535.104.05   CUDA Version: 12.2     |\n",
-            "|-----------------------------------------+----------------------+----------------------+\n",
-            "| GPU  Name                 Persistence-M | Bus-Id        Disp.A | Volatile Uncorr. ECC |\n",
-            "| Fan  Temp   Perf          Pwr:Usage/Cap |         Memory-Usage | GPU-Util  Compute M. |\n",
-            "|                                         |                      |               MIG M. |\n",
-            "|=========================================+======================+======================|\n",
-            "|   0  Tesla T4                       Off | 00000000:00:04.0 Off |                    0 |\n",
-            "| N/A   65C    P0              71W /  70W |   2849MiB / 15360MiB |     58%      Default |\n",
-            "|                                         |                      |                  N/A |\n",
-            "+-----------------------------------------+----------------------+----------------------+\n",
-            "                                                                                         \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| Processes:                                                                            |\n",
-            "|  GPU   GI   CI        PID   Type   Process name                            GPU Memory |\n",
-            "|        ID   ID                                                             Usage      |\n",
-            "|=======================================================================================|\n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "(21767, 1) (28480, 2)\n",
-            "CPU times: user 6.25 s, sys: 100 ms, total: 6.35 s\n",
-            "Wall time: 6.37 s\n"
+            "(30494866, 2)\n",
+            "CPU times: user 16.3 s, sys: 1.31 s, total: 17.6 s\n",
+            "Wall time: 19.2 s\n"
           ]
+        },
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "                       s                      d\n",
+              "0  116374117927631468606  101765416973555767821\n",
+              "1  112188647432305746617  107727150903234299458\n",
+              "2  116719211656774388392  100432456209427807893\n",
+              "3  117421021456205115327  101096322838605097368\n",
+              "4  116407635616074189669  113556266482860931616"
+            ],
+            "text/html": [
+              "\n",
+              "  <div id=\"df-3ebd6e7c-2ff6-495a-b04b-43bd23ea7c91\" class=\"colab-df-container\">\n",
+              "    <div>\n",
+              "<style scoped>\n",
+              "    .dataframe tbody tr th:only-of-type {\n",
+              "        vertical-align: middle;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe tbody tr th {\n",
+              "        vertical-align: top;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe thead th {\n",
+              "        text-align: right;\n",
+              "    }\n",
+              "</style>\n",
+              "<table border=\"1\" class=\"dataframe\">\n",
+              "  <thead>\n",
+              "    <tr style=\"text-align: right;\">\n",
+              "      <th></th>\n",
+              "      <th>s</th>\n",
+              "      <th>d</th>\n",
+              "    </tr>\n",
+              "  </thead>\n",
+              "  <tbody>\n",
+              "    <tr>\n",
+              "      <th>0</th>\n",
+              "      <td>116374117927631468606</td>\n",
+              "      <td>101765416973555767821</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>1</th>\n",
+              "      <td>112188647432305746617</td>\n",
+              "      <td>107727150903234299458</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>2</th>\n",
+              "      <td>116719211656774388392</td>\n",
+              "      <td>100432456209427807893</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>3</th>\n",
+              "      <td>117421021456205115327</td>\n",
+              "      <td>101096322838605097368</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>4</th>\n",
+              "      <td>116407635616074189669</td>\n",
+              "      <td>113556266482860931616</td>\n",
+              "    </tr>\n",
+              "  </tbody>\n",
+              "</table>\n",
+              "</div>\n",
+              "    <div class=\"colab-df-buttons\">\n",
+              "\n",
+              "  <div class=\"colab-df-container\">\n",
+              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-3ebd6e7c-2ff6-495a-b04b-43bd23ea7c91')\"\n",
+              "            title=\"Convert this dataframe to an interactive table.\"\n",
+              "            style=\"display:none;\">\n",
+              "\n",
+              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
+              "    <path d=\"M120-120v-720h720v720H120Zm60-500h600v-160H180v160Zm220 220h160v-160H400v160Zm0 220h160v-160H400v160ZM180-400h160v-160H180v160Zm440 0h160v-160H620v160ZM180-180h160v-160H180v160Zm440 0h160v-160H620v160Z\"/>\n",
+              "  </svg>\n",
+              "    </button>\n",
+              "\n",
+              "  <style>\n",
+              "    .colab-df-container {\n",
+              "      display:flex;\n",
+              "      gap: 12px;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-convert {\n",
+              "      background-color: #E8F0FE;\n",
+              "      border: none;\n",
+              "      border-radius: 50%;\n",
+              "      cursor: pointer;\n",
+              "      display: none;\n",
+              "      fill: #1967D2;\n",
+              "      height: 32px;\n",
+              "      padding: 0 0 0 0;\n",
+              "      width: 32px;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-convert:hover {\n",
+              "      background-color: #E2EBFA;\n",
+              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
+              "      fill: #174EA6;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-buttons div {\n",
+              "      margin-bottom: 4px;\n",
+              "    }\n",
+              "\n",
+              "    [theme=dark] .colab-df-convert {\n",
+              "      background-color: #3B4455;\n",
+              "      fill: #D2E3FC;\n",
+              "    }\n",
+              "\n",
+              "    [theme=dark] .colab-df-convert:hover {\n",
+              "      background-color: #434B5C;\n",
+              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
+              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
+              "      fill: #FFFFFF;\n",
+              "    }\n",
+              "  </style>\n",
+              "\n",
+              "    <script>\n",
+              "      const buttonEl =\n",
+              "        document.querySelector('#df-3ebd6e7c-2ff6-495a-b04b-43bd23ea7c91 button.colab-df-convert');\n",
+              "      buttonEl.style.display =\n",
+              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
+              "\n",
+              "      async function convertToInteractive(key) {\n",
+              "        const element = document.querySelector('#df-3ebd6e7c-2ff6-495a-b04b-43bd23ea7c91');\n",
+              "        const dataTable =\n",
+              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
+              "                                                    [key], {});\n",
+              "        if (!dataTable) return;\n",
+              "\n",
+              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
+              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
+              "          + ' to learn more about interactive tables.';\n",
+              "        element.innerHTML = '';\n",
+              "        dataTable['output_type'] = 'display_data';\n",
+              "        await google.colab.output.renderOutput(dataTable, element);\n",
+              "        const docLink = document.createElement('div');\n",
+              "        docLink.innerHTML = docLinkHtml;\n",
+              "        element.appendChild(docLink);\n",
+              "      }\n",
+              "    </script>\n",
+              "  </div>\n",
+              "\n",
+              "\n",
+              "<div id=\"df-f2cf4e42-fc0b-4dd2-8440-3150bc412292\">\n",
+              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-f2cf4e42-fc0b-4dd2-8440-3150bc412292')\"\n",
+              "            title=\"Suggest charts\"\n",
+              "            style=\"display:none;\">\n",
+              "\n",
+              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
+              "     width=\"24px\">\n",
+              "    <g>\n",
+              "        <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
+              "    </g>\n",
+              "</svg>\n",
+              "  </button>\n",
+              "\n",
+              "<style>\n",
+              "  .colab-df-quickchart {\n",
+              "      --bg-color: #E8F0FE;\n",
+              "      --fill-color: #1967D2;\n",
+              "      --hover-bg-color: #E2EBFA;\n",
+              "      --hover-fill-color: #174EA6;\n",
+              "      --disabled-fill-color: #AAA;\n",
+              "      --disabled-bg-color: #DDD;\n",
+              "  }\n",
+              "\n",
+              "  [theme=dark] .colab-df-quickchart {\n",
+              "      --bg-color: #3B4455;\n",
+              "      --fill-color: #D2E3FC;\n",
+              "      --hover-bg-color: #434B5C;\n",
+              "      --hover-fill-color: #FFFFFF;\n",
+              "      --disabled-bg-color: #3B4455;\n",
+              "      --disabled-fill-color: #666;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart {\n",
+              "    background-color: var(--bg-color);\n",
+              "    border: none;\n",
+              "    border-radius: 50%;\n",
+              "    cursor: pointer;\n",
+              "    display: none;\n",
+              "    fill: var(--fill-color);\n",
+              "    height: 32px;\n",
+              "    padding: 0;\n",
+              "    width: 32px;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart:hover {\n",
+              "    background-color: var(--hover-bg-color);\n",
+              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
+              "    fill: var(--button-hover-fill-color);\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart-complete:disabled,\n",
+              "  .colab-df-quickchart-complete:disabled:hover {\n",
+              "    background-color: var(--disabled-bg-color);\n",
+              "    fill: var(--disabled-fill-color);\n",
+              "    box-shadow: none;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-spinner {\n",
+              "    border: 2px solid var(--fill-color);\n",
+              "    border-color: transparent;\n",
+              "    border-bottom-color: var(--fill-color);\n",
+              "    animation:\n",
+              "      spin 1s steps(1) infinite;\n",
+              "  }\n",
+              "\n",
+              "  @keyframes spin {\n",
+              "    0% {\n",
+              "      border-color: transparent;\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "      border-left-color: var(--fill-color);\n",
+              "    }\n",
+              "    20% {\n",
+              "      border-color: transparent;\n",
+              "      border-left-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "    }\n",
+              "    30% {\n",
+              "      border-color: transparent;\n",
+              "      border-left-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "      border-right-color: var(--fill-color);\n",
+              "    }\n",
+              "    40% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "    }\n",
+              "    60% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "    }\n",
+              "    80% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "    }\n",
+              "    90% {\n",
+              "      border-color: transparent;\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "    }\n",
+              "  }\n",
+              "</style>\n",
+              "\n",
+              "  <script>\n",
+              "    async function quickchart(key) {\n",
+              "      const quickchartButtonEl =\n",
+              "        document.querySelector('#' + key + ' button');\n",
+              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
+              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
+              "      try {\n",
+              "        const charts = await google.colab.kernel.invokeFunction(\n",
+              "            'suggestCharts', [key], {});\n",
+              "      } catch (error) {\n",
+              "        console.error('Error during call to suggestCharts:', error);\n",
+              "      }\n",
+              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
+              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
+              "    }\n",
+              "    (() => {\n",
+              "      let quickchartButtonEl =\n",
+              "        document.querySelector('#df-f2cf4e42-fc0b-4dd2-8440-3150bc412292 button');\n",
+              "      quickchartButtonEl.style.display =\n",
+              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
+              "    })();\n",
+              "  </script>\n",
+              "</div>\n",
+              "\n",
+              "    </div>\n",
+              "  </div>\n"
+            ],
+            "application/vnd.google.colaboratory.intrinsic+json": {
+              "type": "dataframe",
+              "summary": "{\n  \"name\": \"get_ipython()\",\n  \"rows\": 5,\n  \"fields\": [\n    {\n      \"column\": \"s\",\n      \"properties\": {\n        \"dtype\": \"string\",\n        \"num_unique_values\": 5,\n        \"samples\": [\n          \"112188647432305746617\",\n          \"116407635616074189669\",\n          \"116719211656774388392\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"d\",\n      \"properties\": {\n        \"dtype\": \"string\",\n        \"num_unique_values\": 5,\n        \"samples\": [\n          \"107727150903234299458\",\n          \"113556266482860931616\",\n          \"100432456209427807893\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
+            }
+          },
+          "metadata": {},
+          "execution_count": 25
         }
-      ]
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "co_gdf = co_g.nodes(lambda g: cudf.DataFrame(g._nodes)).edges(lambda g: cudf.DataFrame(g._edges))\n",
-        "! nvidia-smi\n",
-        "for i in range(10):\n",
-        "  out = co_gdf.chain([ n({'id': 1}), e_forward(hops=4)])\n",
-        "! nvidia-smi\n",
-        "print(out._nodes.shape, out._edges.shape)\n",
-        "del co_gdf\n",
-        "del out"
       ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "buutj-ZjhrEe",
-        "outputId": "ae11addd-6bea-44e9-81c0-b431e1db8089"
-      },
-      "execution_count": null,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "Mon Dec 25 06:26:04 2023       \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| NVIDIA-SMI 535.104.05             Driver Version: 535.104.05   CUDA Version: 12.2     |\n",
-            "|-----------------------------------------+----------------------+----------------------+\n",
-            "| GPU  Name                 Persistence-M | Bus-Id        Disp.A | Volatile Uncorr. ECC |\n",
-            "| Fan  Temp   Perf          Pwr:Usage/Cap |         Memory-Usage | GPU-Util  Compute M. |\n",
-            "|                                         |                      |               MIG M. |\n",
-            "|=========================================+======================+======================|\n",
-            "|   0  Tesla T4                       Off | 00000000:00:04.0 Off |                    0 |\n",
-            "| N/A   61C    P0              29W /  70W |   1927MiB / 15360MiB |     36%      Default |\n",
-            "|                                         |                      |                  N/A |\n",
-            "+-----------------------------------------+----------------------+----------------------+\n",
-            "                                                                                         \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| Processes:                                                                            |\n",
-            "|  GPU   GI   CI        PID   Type   Process name                            GPU Memory |\n",
-            "|        ID   ID                                                             Usage      |\n",
-            "|=======================================================================================|\n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "Mon Dec 25 06:26:13 2023       \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| NVIDIA-SMI 535.104.05             Driver Version: 535.104.05   CUDA Version: 12.2     |\n",
-            "|-----------------------------------------+----------------------+----------------------+\n",
-            "| GPU  Name                 Persistence-M | Bus-Id        Disp.A | Volatile Uncorr. ECC |\n",
-            "| Fan  Temp   Perf          Pwr:Usage/Cap |         Memory-Usage | GPU-Util  Compute M. |\n",
-            "|                                         |                      |               MIG M. |\n",
-            "|=========================================+======================+======================|\n",
-            "|   0  Tesla T4                       Off | 00000000:00:04.0 Off |                    0 |\n",
-            "| N/A   65C    P0              71W /  70W |   2931MiB / 15360MiB |     90%      Default |\n",
-            "|                                         |                      |                  N/A |\n",
-            "+-----------------------------------------+----------------------+----------------------+\n",
-            "                                                                                         \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| Processes:                                                                            |\n",
-            "|  GPU   GI   CI        PID   Type   Process name                            GPU Memory |\n",
-            "|        ID   ID                                                             Usage      |\n",
-            "|=======================================================================================|\n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "(718640, 1) (2210961, 2)\n",
-            "CPU times: user 9.01 s, sys: 1.03 s, total: 10 s\n",
-            "Wall time: 9.84 s\n"
-          ]
-        }
-      ]
-    },
-    {
-      "cell_type": "code",
       "source": [
         "%%time\n",
-        "co_gdf = co_g.nodes(lambda g: cudf.DataFrame(g._nodes)).edges(lambda g: cudf.DataFrame(g._edges))\n",
-        "! nvidia-smi\n",
-        "for i in range(10):\n",
-        "  out = co_gdf.chain([ n({'id': 1}), e_forward(hops=5)])\n",
-        "! nvidia-smi\n",
-        "print(out._nodes.shape, out._edges.shape)\n",
-        "del co_gdf\n",
-        "del out"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "bK4C9Ly0hso-",
-        "outputId": "8a9a32ab-03e2-42b4-8b71-2bcf797b31b1"
-      },
-      "execution_count": null,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "Mon Dec 25 06:27:18 2023       \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| NVIDIA-SMI 535.104.05             Driver Version: 535.104.05   CUDA Version: 12.2     |\n",
-            "|-----------------------------------------+----------------------+----------------------+\n",
-            "| GPU  Name                 Persistence-M | Bus-Id        Disp.A | Volatile Uncorr. ECC |\n",
-            "| Fan  Temp   Perf          Pwr:Usage/Cap |         Memory-Usage | GPU-Util  Compute M. |\n",
-            "|                                         |                      |               MIG M. |\n",
-            "|=========================================+======================+======================|\n",
-            "|   0  Tesla T4                       Off | 00000000:00:04.0 Off |                    0 |\n",
-            "| N/A   60C    P0              29W /  70W |   1927MiB / 15360MiB |     28%      Default |\n",
-            "|                                         |                      |                  N/A |\n",
-            "+-----------------------------------------+----------------------+----------------------+\n",
-            "                                                                                         \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| Processes:                                                                            |\n",
-            "|  GPU   GI   CI        PID   Type   Process name                            GPU Memory |\n",
-            "|        ID   ID                                                             Usage      |\n",
-            "|=======================================================================================|\n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "Mon Dec 25 06:27:57 2023       \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| NVIDIA-SMI 535.104.05             Driver Version: 535.104.05   CUDA Version: 12.2     |\n",
-            "|-----------------------------------------+----------------------+----------------------+\n",
-            "| GPU  Name                 Persistence-M | Bus-Id        Disp.A | Volatile Uncorr. ECC |\n",
-            "| Fan  Temp   Perf          Pwr:Usage/Cap |         Memory-Usage | GPU-Util  Compute M. |\n",
-            "|                                         |                      |               MIG M. |\n",
-            "|=========================================+======================+======================|\n",
-            "|   0  Tesla T4                       Off | 00000000:00:04.0 Off |                    0 |\n",
-            "| N/A   72C    P0              43W /  70W |   4351MiB / 15360MiB |    100%      Default |\n",
-            "|                                         |                      |                  N/A |\n",
-            "+-----------------------------------------+----------------------+----------------------+\n",
-            "                                                                                         \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| Processes:                                                                            |\n",
-            "|  GPU   GI   CI        PID   Type   Process name                            GPU Memory |\n",
-            "|        ID   ID                                                             Usage      |\n",
-            "|=======================================================================================|\n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "(3041556, 1) (47622917, 2)\n",
-            "CPU times: user 34.9 s, sys: 4.76 s, total: 39.6 s\n",
-            "Wall time: 39.2 s\n"
-          ]
-        }
+        "ge_df = pd.read_csv('gplus_combined.txt', sep=' ', names=['s', 'd'])\n",
+        "print(ge_df.shape)\n",
+        "ge_df.head(5)"
       ]
     },
     {
       "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "co_gdf = co_g.nodes(lambda g: cudf.DataFrame(g._nodes)).edges(lambda g: cudf.DataFrame(g._edges))\n",
-        "out = co_gdf.chain([ n({'id': 1}), e_forward(hops=6)])._nodes\n",
-        "print(out.shape)\n",
-        "del co_gdf\n",
-        "del out"
-      ],
-      "metadata": {
-        "id": "qrga-la0hwhh"
-      },
-      "execution_count": null,
-      "outputs": []
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "!lscpu\n"
-      ],
+      "execution_count": 26,
       "metadata": {
+        "id": "w5YkN-nLK6UV",
         "colab": {
-          "base_uri": "https://localhost:8080/"
+          "base_uri": "https://localhost:8080/",
+          "height": 260
         },
-        "id": "eiXFImxF-rzw",
-        "outputId": "b807cc3d-ed1a-4bef-c6e0-bfc2df7356ff"
+        "outputId": "89c4b0a5-a355-4558-8b3c-187b0efe471a"
       },
-      "execution_count": null,
       "outputs": [
         {
           "output_type": "stream",
           "name": "stdout",
           "text": [
-            "Architecture:            x86_64\n",
-            "  CPU op-mode(s):        32-bit, 64-bit\n",
-            "  Address sizes:         46 bits physical, 48 bits virtual\n",
-            "  Byte Order:            Little Endian\n",
-            "CPU(s):                  2\n",
-            "  On-line CPU(s) list:   0,1\n",
-            "Vendor ID:               GenuineIntel\n",
-            "  Model name:            Intel(R) Xeon(R) CPU @ 2.20GHz\n",
-            "    CPU family:          6\n",
-            "    Model:               79\n",
-            "    Thread(s) per core:  2\n",
-            "    Core(s) per socket:  1\n",
-            "    Socket(s):           1\n",
-            "    Stepping:            0\n",
-            "    BogoMIPS:            4399.99\n",
-            "    Flags:               fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clf\n",
-            "                         lush mmx fxsr sse sse2 ss ht syscall nx pdpe1gb rdtscp lm constant_tsc rep_\n",
-            "                         good nopl xtopology nonstop_tsc cpuid tsc_known_freq pni pclmulqdq ssse3 fm\n",
-            "                         a cx16 pcid sse4_1 sse4_2 x2apic movbe popcnt aes xsave avx f16c rdrand hyp\n",
-            "                         ervisor lahf_lm abm 3dnowprefetch invpcid_single ssbd ibrs ibpb stibp fsgsb\n",
-            "                         ase tsc_adjust bmi1 hle avx2 smep bmi2 erms invpcid rtm rdseed adx smap xsa\n",
-            "                         veopt arat md_clear arch_capabilities\n",
-            "Virtualization features: \n",
-            "  Hypervisor vendor:     KVM\n",
-            "  Virtualization type:   full\n",
-            "Caches (sum of all):     \n",
-            "  L1d:                   32 KiB (1 instance)\n",
-            "  L1i:                   32 KiB (1 instance)\n",
-            "  L2:                    256 KiB (1 instance)\n",
-            "  L3:                    55 MiB (1 instance)\n",
-            "NUMA:                    \n",
-            "  NUMA node(s):          1\n",
-            "  NUMA node0 CPU(s):     0,1\n",
-            "Vulnerabilities:         \n",
-            "  Gather data sampling:  Not affected\n",
-            "  Itlb multihit:         Not affected\n",
-            "  L1tf:                  Mitigation; PTE Inversion\n",
-            "  Mds:                   Vulnerable; SMT Host state unknown\n",
-            "  Meltdown:              Vulnerable\n",
-            "  Mmio stale data:       Vulnerable\n",
-            "  Retbleed:              Vulnerable\n",
-            "  Spec rstack overflow:  Not affected\n",
-            "  Spec store bypass:     Vulnerable\n",
-            "  Spectre v1:            Vulnerable: __user pointer sanitization and usercopy barriers only; no swap\n",
-            "                         gs barriers\n",
-            "  Spectre v2:            Vulnerable, IBPB: disabled, STIBP: disabled, PBRSB-eIBRS: Not affected\n",
-            "  Srbds:                 Not affected\n",
-            "  Tsx async abort:       Vulnerable\n"
+            "(30494866, 2) (107614, 1)\n",
+            "CPU times: user 5.14 s, sys: 1.08 s, total: 6.22 s\n",
+            "Wall time: 6.27 s\n"
           ]
+        },
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "                      id\n",
+              "0  116374117927631468606\n",
+              "1  112188647432305746617\n",
+              "2  116719211656774388392\n",
+              "3  117421021456205115327\n",
+              "4  116407635616074189669"
+            ],
+            "text/html": [
+              "\n",
+              "  <div id=\"df-e1c8493b-d264-4d1a-a57f-ca488023b123\" class=\"colab-df-container\">\n",
+              "    <div>\n",
+              "<style scoped>\n",
+              "    .dataframe tbody tr th:only-of-type {\n",
+              "        vertical-align: middle;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe tbody tr th {\n",
+              "        vertical-align: top;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe thead th {\n",
+              "        text-align: right;\n",
+              "    }\n",
+              "</style>\n",
+              "<table border=\"1\" class=\"dataframe\">\n",
+              "  <thead>\n",
+              "    <tr style=\"text-align: right;\">\n",
+              "      <th></th>\n",
+              "      <th>id</th>\n",
+              "    </tr>\n",
+              "  </thead>\n",
+              "  <tbody>\n",
+              "    <tr>\n",
+              "      <th>0</th>\n",
+              "      <td>116374117927631468606</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>1</th>\n",
+              "      <td>112188647432305746617</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>2</th>\n",
+              "      <td>116719211656774388392</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>3</th>\n",
+              "      <td>117421021456205115327</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>4</th>\n",
+              "      <td>116407635616074189669</td>\n",
+              "    </tr>\n",
+              "  </tbody>\n",
+              "</table>\n",
+              "</div>\n",
+              "    <div class=\"colab-df-buttons\">\n",
+              "\n",
+              "  <div class=\"colab-df-container\">\n",
+              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-e1c8493b-d264-4d1a-a57f-ca488023b123')\"\n",
+              "            title=\"Convert this dataframe to an interactive table.\"\n",
+              "            style=\"display:none;\">\n",
+              "\n",
+              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
+              "    <path d=\"M120-120v-720h720v720H120Zm60-500h600v-160H180v160Zm220 220h160v-160H400v160Zm0 220h160v-160H400v160ZM180-400h160v-160H180v160Zm440 0h160v-160H620v160ZM180-180h160v-160H180v160Zm440 0h160v-160H620v160Z\"/>\n",
+              "  </svg>\n",
+              "    </button>\n",
+              "\n",
+              "  <style>\n",
+              "    .colab-df-container {\n",
+              "      display:flex;\n",
+              "      gap: 12px;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-convert {\n",
+              "      background-color: #E8F0FE;\n",
+              "      border: none;\n",
+              "      border-radius: 50%;\n",
+              "      cursor: pointer;\n",
+              "      display: none;\n",
+              "      fill: #1967D2;\n",
+              "      height: 32px;\n",
+              "      padding: 0 0 0 0;\n",
+              "      width: 32px;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-convert:hover {\n",
+              "      background-color: #E2EBFA;\n",
+              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
+              "      fill: #174EA6;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-buttons div {\n",
+              "      margin-bottom: 4px;\n",
+              "    }\n",
+              "\n",
+              "    [theme=dark] .colab-df-convert {\n",
+              "      background-color: #3B4455;\n",
+              "      fill: #D2E3FC;\n",
+              "    }\n",
+              "\n",
+              "    [theme=dark] .colab-df-convert:hover {\n",
+              "      background-color: #434B5C;\n",
+              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
+              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
+              "      fill: #FFFFFF;\n",
+              "    }\n",
+              "  </style>\n",
+              "\n",
+              "    <script>\n",
+              "      const buttonEl =\n",
+              "        document.querySelector('#df-e1c8493b-d264-4d1a-a57f-ca488023b123 button.colab-df-convert');\n",
+              "      buttonEl.style.display =\n",
+              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
+              "\n",
+              "      async function convertToInteractive(key) {\n",
+              "        const element = document.querySelector('#df-e1c8493b-d264-4d1a-a57f-ca488023b123');\n",
+              "        const dataTable =\n",
+              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
+              "                                                    [key], {});\n",
+              "        if (!dataTable) return;\n",
+              "\n",
+              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
+              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
+              "          + ' to learn more about interactive tables.';\n",
+              "        element.innerHTML = '';\n",
+              "        dataTable['output_type'] = 'display_data';\n",
+              "        await google.colab.output.renderOutput(dataTable, element);\n",
+              "        const docLink = document.createElement('div');\n",
+              "        docLink.innerHTML = docLinkHtml;\n",
+              "        element.appendChild(docLink);\n",
+              "      }\n",
+              "    </script>\n",
+              "  </div>\n",
+              "\n",
+              "\n",
+              "<div id=\"df-2b724962-26c5-4f5a-a2ac-f86f38414e16\">\n",
+              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-2b724962-26c5-4f5a-a2ac-f86f38414e16')\"\n",
+              "            title=\"Suggest charts\"\n",
+              "            style=\"display:none;\">\n",
+              "\n",
+              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
+              "     width=\"24px\">\n",
+              "    <g>\n",
+              "        <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
+              "    </g>\n",
+              "</svg>\n",
+              "  </button>\n",
+              "\n",
+              "<style>\n",
+              "  .colab-df-quickchart {\n",
+              "      --bg-color: #E8F0FE;\n",
+              "      --fill-color: #1967D2;\n",
+              "      --hover-bg-color: #E2EBFA;\n",
+              "      --hover-fill-color: #174EA6;\n",
+              "      --disabled-fill-color: #AAA;\n",
+              "      --disabled-bg-color: #DDD;\n",
+              "  }\n",
+              "\n",
+              "  [theme=dark] .colab-df-quickchart {\n",
+              "      --bg-color: #3B4455;\n",
+              "      --fill-color: #D2E3FC;\n",
+              "      --hover-bg-color: #434B5C;\n",
+              "      --hover-fill-color: #FFFFFF;\n",
+              "      --disabled-bg-color: #3B4455;\n",
+              "      --disabled-fill-color: #666;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart {\n",
+              "    background-color: var(--bg-color);\n",
+              "    border: none;\n",
+              "    border-radius: 50%;\n",
+              "    cursor: pointer;\n",
+              "    display: none;\n",
+              "    fill: var(--fill-color);\n",
+              "    height: 32px;\n",
+              "    padding: 0;\n",
+              "    width: 32px;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart:hover {\n",
+              "    background-color: var(--hover-bg-color);\n",
+              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
+              "    fill: var(--button-hover-fill-color);\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart-complete:disabled,\n",
+              "  .colab-df-quickchart-complete:disabled:hover {\n",
+              "    background-color: var(--disabled-bg-color);\n",
+              "    fill: var(--disabled-fill-color);\n",
+              "    box-shadow: none;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-spinner {\n",
+              "    border: 2px solid var(--fill-color);\n",
+              "    border-color: transparent;\n",
+              "    border-bottom-color: var(--fill-color);\n",
+              "    animation:\n",
+              "      spin 1s steps(1) infinite;\n",
+              "  }\n",
+              "\n",
+              "  @keyframes spin {\n",
+              "    0% {\n",
+              "      border-color: transparent;\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "      border-left-color: var(--fill-color);\n",
+              "    }\n",
+              "    20% {\n",
+              "      border-color: transparent;\n",
+              "      border-left-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "    }\n",
+              "    30% {\n",
+              "      border-color: transparent;\n",
+              "      border-left-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "      border-right-color: var(--fill-color);\n",
+              "    }\n",
+              "    40% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "    }\n",
+              "    60% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "    }\n",
+              "    80% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "    }\n",
+              "    90% {\n",
+              "      border-color: transparent;\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "    }\n",
+              "  }\n",
+              "</style>\n",
+              "\n",
+              "  <script>\n",
+              "    async function quickchart(key) {\n",
+              "      const quickchartButtonEl =\n",
+              "        document.querySelector('#' + key + ' button');\n",
+              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
+              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
+              "      try {\n",
+              "        const charts = await google.colab.kernel.invokeFunction(\n",
+              "            'suggestCharts', [key], {});\n",
+              "      } catch (error) {\n",
+              "        console.error('Error during call to suggestCharts:', error);\n",
+              "      }\n",
+              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
+              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
+              "    }\n",
+              "    (() => {\n",
+              "      let quickchartButtonEl =\n",
+              "        document.querySelector('#df-2b724962-26c5-4f5a-a2ac-f86f38414e16 button');\n",
+              "      quickchartButtonEl.style.display =\n",
+              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
+              "    })();\n",
+              "  </script>\n",
+              "</div>\n",
+              "\n",
+              "    </div>\n",
+              "  </div>\n"
+            ],
+            "application/vnd.google.colaboratory.intrinsic+json": {
+              "type": "dataframe",
+              "summary": "{\n  \"name\": \"get_ipython()\",\n  \"rows\": 5,\n  \"fields\": [\n    {\n      \"column\": \"id\",\n      \"properties\": {\n        \"dtype\": \"string\",\n        \"num_unique_values\": 5,\n        \"samples\": [\n          \"112188647432305746617\",\n          \"116407635616074189669\",\n          \"116719211656774388392\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
+            }
+          },
+          "metadata": {},
+          "execution_count": 26
         }
-      ]
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "!free -h\n"
       ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "wJohLi58-sN5",
-        "outputId": "c3e144f6-c19a-4c68-e867-f5e7fa2e9df4"
-      },
-      "execution_count": null,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "               total        used        free      shared  buff/cache   available\n",
-            "Mem:            12Gi       717Mi       8.0Gi       1.0Mi       3.9Gi        11Gi\n",
-            "Swap:             0B          0B          0B\n"
-          ]
-        }
-      ]
-    },
-    {
-      "cell_type": "code",
       "source": [
         "%%time\n",
-        "start_nodes = pd.DataFrame({'id': [1]})\n",
-        "! nvidia-smi\n",
-        "for i in range(1):\n",
-        "  g2 = co_g.hop(\n",
-        "      nodes=start_nodes,\n",
-        "      direction='forward',\n",
-        "      hops=1)\n",
-        "! nvidia-smi\n",
-        "print(g2._nodes.shape, g2._edges.shape)\n",
-        "#del start_nodes\n",
-        "#del co_gdf\n",
-        "#del g2"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "zak4Inhco5il",
-        "outputId": "30bcf2bc-853e-4e5e-8c57-ba0cd9429554"
-      },
-      "execution_count": null,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "Tue Dec 26 01:01:43 2023       \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| NVIDIA-SMI 535.104.05             Driver Version: 535.104.05   CUDA Version: 12.2     |\n",
-            "|-----------------------------------------+----------------------+----------------------+\n",
-            "| GPU  Name                 Persistence-M | Bus-Id        Disp.A | Volatile Uncorr. ECC |\n",
-            "| Fan  Temp   Perf          Pwr:Usage/Cap |         Memory-Usage | GPU-Util  Compute M. |\n",
-            "|                                         |                      |               MIG M. |\n",
-            "|=========================================+======================+======================|\n",
-            "|   0  Tesla T4                       Off | 00000000:00:04.0 Off |                    0 |\n",
-            "| N/A   64C    P0              30W /  70W |   2821MiB / 15360MiB |      0%      Default |\n",
-            "|                                         |                      |                  N/A |\n",
-            "+-----------------------------------------+----------------------+----------------------+\n",
-            "                                                                                         \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| Processes:                                                                            |\n",
-            "|  GPU   GI   CI        PID   Type   Process name                            GPU Memory |\n",
-            "|        ID   ID                                                             Usage      |\n",
-            "|=======================================================================================|\n",
-            "+---------------------------------------------------------------------------------------+\n"
-          ]
-        }
+        "gg = graphistry.edges(ge_df, 's', 'd').materialize_nodes()\n",
+        "gg = graphistry.edges(ge_df, 's', 'd').nodes(gg._nodes, 'id')\n",
+        "print(gg._edges.shape, gg._nodes.shape)\n",
+        "gg._nodes.head(5)"
       ]
     },
     {
       "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "start_nodes = cudf.DataFrame({'id': [1]})\n",
-        "co_gdf = co_g.nodes(lambda g: cudf.DataFrame(g._nodes)).edges(lambda g: cudf.DataFrame(g._edges))\n",
-        "! nvidia-smi\n",
-        "for i in range(10):\n",
-        "  g2 = co_gdf.hop(\n",
-        "      nodes=start_nodes,\n",
-        "      direction='forward',\n",
-        "      hops=1)\n",
-        "! nvidia-smi\n",
-        "print(g2._nodes.shape, g2._edges.shape)\n",
-        "del start_nodes\n",
-        "del co_gdf\n",
-        "del g2"
-      ],
+      "execution_count": 27,
       "metadata": {
-        "id": "-SmFlCBS_Bgx",
+        "id": "NKtz54uELX-8",
         "colab": {
-          "base_uri": "https://localhost:8080/"
+          "base_uri": "https://localhost:8080/",
+          "height": 116
         },
-        "outputId": "d2326cf7-3ea6-4f99-9548-f2e98ece59a4"
+        "outputId": "f4b28841-62bc-42cd-e771-127400a2689e"
       },
-      "execution_count": 16,
       "outputs": [
         {
           "output_type": "stream",
           "name": "stdout",
           "text": [
-            "Tue Dec 26 00:56:45 2023       \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| NVIDIA-SMI 535.104.05             Driver Version: 535.104.05   CUDA Version: 12.2     |\n",
-            "|-----------------------------------------+----------------------+----------------------+\n",
-            "| GPU  Name                 Persistence-M | Bus-Id        Disp.A | Volatile Uncorr. ECC |\n",
-            "| Fan  Temp   Perf          Pwr:Usage/Cap |         Memory-Usage | GPU-Util  Compute M. |\n",
-            "|                                         |                      |               MIG M. |\n",
-            "|=========================================+======================+======================|\n",
-            "|   0  Tesla T4                       Off | 00000000:00:04.0 Off |                    0 |\n",
-            "| N/A   49C    P0              28W /  70W |   1923MiB / 15360MiB |     37%      Default |\n",
-            "|                                         |                      |                  N/A |\n",
-            "+-----------------------------------------+----------------------+----------------------+\n",
-            "                                                                                         \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| Processes:                                                                            |\n",
-            "|  GPU   GI   CI        PID   Type   Process name                            GPU Memory |\n",
-            "|        ID   ID                                                             Usage      |\n",
-            "|=======================================================================================|\n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "Tue Dec 26 00:56:47 2023       \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| NVIDIA-SMI 535.104.05             Driver Version: 535.104.05   CUDA Version: 12.2     |\n",
-            "|-----------------------------------------+----------------------+----------------------+\n",
-            "| GPU  Name                 Persistence-M | Bus-Id        Disp.A | Volatile Uncorr. ECC |\n",
-            "| Fan  Temp   Perf          Pwr:Usage/Cap |         Memory-Usage | GPU-Util  Compute M. |\n",
-            "|                                         |                      |               MIG M. |\n",
-            "|=========================================+======================+======================|\n",
-            "|   0  Tesla T4                       Off | 00000000:00:04.0 Off |                    0 |\n",
-            "| N/A   52C    P0              70W /  70W |   2819MiB / 15360MiB |     79%      Default |\n",
-            "|                                         |                      |                  N/A |\n",
-            "+-----------------------------------------+----------------------+----------------------+\n",
-            "                                                                                         \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| Processes:                                                                            |\n",
-            "|  GPU   GI   CI        PID   Type   Process name                            GPU Memory |\n",
-            "|        ID   ID                                                             Usage      |\n",
-            "|=======================================================================================|\n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "(12, 1) (11, 2)\n",
-            "CPU times: user 1.6 s, sys: 37.3 ms, total: 1.64 s\n",
-            "Wall time: 1.84 s\n"
+            "CPU times: user 676 ms, sys: 400 ms, total: 1.08 s\n",
+            "Wall time: 1.11 s\n"
           ]
-        }
-      ]
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "start_nodes = cudf.DataFrame({'id': [1]})\n",
-        "co_gdf = co_g.nodes(lambda g: cudf.DataFrame(g._nodes)).edges(lambda g: cudf.DataFrame(g._edges))\n",
-        "! nvidia-smi\n",
-        "for i in range(10):\n",
-        "  g2 = co_gdf.hop(\n",
-        "      nodes=start_nodes,\n",
-        "      direction='forward',\n",
-        "      hops=2)\n",
-        "! nvidia-smi\n",
-        "print(g2._nodes.shape, g2._edges.shape)\n",
-        "del start_nodes\n",
-        "del co_gdf\n",
-        "del g2"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
         },
-        "id": "fjjt3YnYnabv",
-        "outputId": "05762f50-bfe1-4d23-9153-31431418c8e5"
-      },
-      "execution_count": 17,
-      "outputs": [
         {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "Tue Dec 26 00:56:47 2023       \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| NVIDIA-SMI 535.104.05             Driver Version: 535.104.05   CUDA Version: 12.2     |\n",
-            "|-----------------------------------------+----------------------+----------------------+\n",
-            "| GPU  Name                 Persistence-M | Bus-Id        Disp.A | Volatile Uncorr. ECC |\n",
-            "| Fan  Temp   Perf          Pwr:Usage/Cap |         Memory-Usage | GPU-Util  Compute M. |\n",
-            "|                                         |                      |               MIG M. |\n",
-            "|=========================================+======================+======================|\n",
-            "|   0  Tesla T4                       Off | 00000000:00:04.0 Off |                    0 |\n",
-            "| N/A   51C    P0              35W /  70W |   1923MiB / 15360MiB |     59%      Default |\n",
-            "|                                         |                      |                  N/A |\n",
-            "+-----------------------------------------+----------------------+----------------------+\n",
-            "                                                                                         \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| Processes:                                                                            |\n",
-            "|  GPU   GI   CI        PID   Type   Process name                            GPU Memory |\n",
-            "|        ID   ID                                                             Usage      |\n",
-            "|=======================================================================================|\n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "Tue Dec 26 00:56:49 2023       \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| NVIDIA-SMI 535.104.05             Driver Version: 535.104.05   CUDA Version: 12.2     |\n",
-            "|-----------------------------------------+----------------------+----------------------+\n",
-            "| GPU  Name                 Persistence-M | Bus-Id        Disp.A | Volatile Uncorr. ECC |\n",
-            "| Fan  Temp   Perf          Pwr:Usage/Cap |         Memory-Usage | GPU-Util  Compute M. |\n",
-            "|                                         |                      |               MIG M. |\n",
-            "|=========================================+======================+======================|\n",
-            "|   0  Tesla T4                       Off | 00000000:00:04.0 Off |                    0 |\n",
-            "| N/A   53C    P0              59W /  70W |   2821MiB / 15360MiB |     86%      Default |\n",
-            "|                                         |                      |                  N/A |\n",
-            "+-----------------------------------------+----------------------+----------------------+\n",
-            "                                                                                         \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| Processes:                                                                            |\n",
-            "|  GPU   GI   CI        PID   Type   Process name                            GPU Memory |\n",
-            "|        ID   ID                                                             Usage      |\n",
-            "|=======================================================================================|\n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "(391, 1) (461, 2)\n",
-            "CPU times: user 2.32 s, sys: 58.5 ms, total: 2.38 s\n",
-            "Wall time: 2.51 s\n"
-          ]
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "                      id\n",
+              "0  116374117927631468606"
+            ],
+            "text/html": [
+              "\n",
+              "  <div id=\"df-6a2b39a2-c688-4ca6-ace7-1623fcd2fa7f\" class=\"colab-df-container\">\n",
+              "    <div>\n",
+              "<style scoped>\n",
+              "    .dataframe tbody tr th:only-of-type {\n",
+              "        vertical-align: middle;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe tbody tr th {\n",
+              "        vertical-align: top;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe thead th {\n",
+              "        text-align: right;\n",
+              "    }\n",
+              "</style>\n",
+              "<table border=\"1\" class=\"dataframe\">\n",
+              "  <thead>\n",
+              "    <tr style=\"text-align: right;\">\n",
+              "      <th></th>\n",
+              "      <th>id</th>\n",
+              "    </tr>\n",
+              "  </thead>\n",
+              "  <tbody>\n",
+              "    <tr>\n",
+              "      <th>0</th>\n",
+              "      <td>116374117927631468606</td>\n",
+              "    </tr>\n",
+              "  </tbody>\n",
+              "</table>\n",
+              "</div>\n",
+              "    <div class=\"colab-df-buttons\">\n",
+              "\n",
+              "  <div class=\"colab-df-container\">\n",
+              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-6a2b39a2-c688-4ca6-ace7-1623fcd2fa7f')\"\n",
+              "            title=\"Convert this dataframe to an interactive table.\"\n",
+              "            style=\"display:none;\">\n",
+              "\n",
+              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
+              "    <path d=\"M120-120v-720h720v720H120Zm60-500h600v-160H180v160Zm220 220h160v-160H400v160Zm0 220h160v-160H400v160ZM180-400h160v-160H180v160Zm440 0h160v-160H620v160ZM180-180h160v-160H180v160Zm440 0h160v-160H620v160Z\"/>\n",
+              "  </svg>\n",
+              "    </button>\n",
+              "\n",
+              "  <style>\n",
+              "    .colab-df-container {\n",
+              "      display:flex;\n",
+              "      gap: 12px;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-convert {\n",
+              "      background-color: #E8F0FE;\n",
+              "      border: none;\n",
+              "      border-radius: 50%;\n",
+              "      cursor: pointer;\n",
+              "      display: none;\n",
+              "      fill: #1967D2;\n",
+              "      height: 32px;\n",
+              "      padding: 0 0 0 0;\n",
+              "      width: 32px;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-convert:hover {\n",
+              "      background-color: #E2EBFA;\n",
+              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
+              "      fill: #174EA6;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-buttons div {\n",
+              "      margin-bottom: 4px;\n",
+              "    }\n",
+              "\n",
+              "    [theme=dark] .colab-df-convert {\n",
+              "      background-color: #3B4455;\n",
+              "      fill: #D2E3FC;\n",
+              "    }\n",
+              "\n",
+              "    [theme=dark] .colab-df-convert:hover {\n",
+              "      background-color: #434B5C;\n",
+              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
+              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
+              "      fill: #FFFFFF;\n",
+              "    }\n",
+              "  </style>\n",
+              "\n",
+              "    <script>\n",
+              "      const buttonEl =\n",
+              "        document.querySelector('#df-6a2b39a2-c688-4ca6-ace7-1623fcd2fa7f button.colab-df-convert');\n",
+              "      buttonEl.style.display =\n",
+              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
+              "\n",
+              "      async function convertToInteractive(key) {\n",
+              "        const element = document.querySelector('#df-6a2b39a2-c688-4ca6-ace7-1623fcd2fa7f');\n",
+              "        const dataTable =\n",
+              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
+              "                                                    [key], {});\n",
+              "        if (!dataTable) return;\n",
+              "\n",
+              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
+              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
+              "          + ' to learn more about interactive tables.';\n",
+              "        element.innerHTML = '';\n",
+              "        dataTable['output_type'] = 'display_data';\n",
+              "        await google.colab.output.renderOutput(dataTable, element);\n",
+              "        const docLink = document.createElement('div');\n",
+              "        docLink.innerHTML = docLinkHtml;\n",
+              "        element.appendChild(docLink);\n",
+              "      }\n",
+              "    </script>\n",
+              "  </div>\n",
+              "\n",
+              "\n",
+              "    </div>\n",
+              "  </div>\n"
+            ],
+            "application/vnd.google.colaboratory.intrinsic+json": {
+              "type": "dataframe",
+              "summary": "{\n  \"name\": \"get_ipython()\",\n  \"rows\": 1,\n  \"fields\": [\n    {\n      \"column\": \"id\",\n      \"properties\": {\n        \"dtype\": \"string\",\n        \"num_unique_values\": 1,\n        \"samples\": [\n          \"116374117927631468606\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
+            }
+          },
+          "metadata": {},
+          "execution_count": 27
         }
+      ],
+      "source": [
+        "%%time\n",
+        "gg.chain([ n({'id': '116374117927631468606'})])._nodes"
       ]
     },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "on the GPlus data, simpler `chain` operations over several different hops -- **100-200x** speed increases"
+      ],
+      "metadata": {
+        "id": "e4ZchWvrBKdY"
+      }
+    },
     {
       "cell_type": "code",
       "source": [
-        "%%time\n",
-        "start_nodes = cudf.DataFrame({'id': [1]})\n",
-        "co_gdf = co_g.nodes(lambda g: cudf.DataFrame(g._nodes)).edges(lambda g: cudf.DataFrame(g._edges))\n",
-        "! nvidia-smi\n",
-        "for i in range(10):\n",
-        "  g2 = co_gdf.hop(\n",
-        "      nodes=start_nodes,\n",
-        "      direction='forward',\n",
-        "      hops=3)\n",
-        "! nvidia-smi\n",
-        "print(g2._nodes.shape, g2._edges.shape)\n",
-        "del start_nodes\n",
-        "del co_gdf\n",
-        "del g2"
+        "results_df = pd.DataFrame(columns=['hops', 'CPU hop chain time (s)', 'GPU hop chain time (s)', 'n_notation speedup'])\n",
+        "\n",
+        "\n",
+        "for n_hop in [1,2,3,4,5]:\n",
+        "    start_nodes = pd.DataFrame({fg._node: [0]})\n",
+        "    start0 = time.time()\n",
+        "    out = gg.chain([ n({'id': '116374117927631468606'}), e_forward(hops=n_hop)])._nodes\n",
+        "    end0 = time.time()\n",
+        "    T0 = end0-start0\n",
+        "    gg_gdf = gg.nodes(lambda g: cudf.DataFrame(g._nodes)).edges(lambda g: cudf.DataFrame(g._edges))\n",
+        "    start1 = time.time()\n",
+        "    out = gg_gdf.chain([ n({'id': '116374117927631468606'}), e_forward(hops=n_hop)])\n",
+        "    end1 = time.time()\n",
+        "\n",
+        "    del gg_gdf\n",
+        "    del out\n",
+        "    T1 = end1-start1\n",
+        "    # print('\\nCPU',n_hop,'hop chain time:',np.round(T0,4),'\\nGPU',n_hop,'hop chain time:',np.round(T1,4),'\\nspeedup:', np.round(T0/T1,4))\n",
+        "\n",
+        "    new_row = pd.DataFrame({\n",
+        "        'hops': [n_hop],\n",
+        "        'CPU hop chain time (s)': [np.round(T0, 4)],\n",
+        "        'GPU hop chain time (s)': [np.round(T1, 4)],\n",
+        "        'n_notation speedup': [np.round(T0 / T1, 4)]\n",
+        "    })\n",
+        "\n",
+        "    results_df = pd.concat([results_df, new_row], ignore_index=True)\n",
+        "\n",
+        "(results_df.T)"
       ],
       "metadata": {
         "colab": {
-          "base_uri": "https://localhost:8080/"
+          "base_uri": "https://localhost:8080/",
+          "height": 175
         },
-        "id": "oIouuORgnbcY",
-        "outputId": "f07abe4c-5137-4ee3-935a-afbb2c5eaa1e"
+        "id": "fTnU8MLr8tV5",
+        "outputId": "203eb5bf-9d95-4557-f35e-7ef2274424c5"
       },
-      "execution_count": 18,
+      "execution_count": 28,
       "outputs": [
         {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "Tue Dec 26 00:56:50 2023       \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| NVIDIA-SMI 535.104.05             Driver Version: 535.104.05   CUDA Version: 12.2     |\n",
-            "|-----------------------------------------+----------------------+----------------------+\n",
-            "| GPU  Name                 Persistence-M | Bus-Id        Disp.A | Volatile Uncorr. ECC |\n",
-            "| Fan  Temp   Perf          Pwr:Usage/Cap |         Memory-Usage | GPU-Util  Compute M. |\n",
-            "|                                         |                      |               MIG M. |\n",
-            "|=========================================+======================+======================|\n",
-            "|   0  Tesla T4                       Off | 00000000:00:04.0 Off |                    0 |\n",
-            "| N/A   52C    P0              36W /  70W |   1925MiB / 15360MiB |     55%      Default |\n",
-            "|                                         |                      |                  N/A |\n",
-            "+-----------------------------------------+----------------------+----------------------+\n",
-            "                                                                                         \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| Processes:                                                                            |\n",
-            "|  GPU   GI   CI        PID   Type   Process name                            GPU Memory |\n",
-            "|        ID   ID                                                             Usage      |\n",
-            "|=======================================================================================|\n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "Tue Dec 26 00:56:53 2023       \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| NVIDIA-SMI 535.104.05             Driver Version: 535.104.05   CUDA Version: 12.2     |\n",
-            "|-----------------------------------------+----------------------+----------------------+\n",
-            "| GPU  Name                 Persistence-M | Bus-Id        Disp.A | Volatile Uncorr. ECC |\n",
-            "| Fan  Temp   Perf          Pwr:Usage/Cap |         Memory-Usage | GPU-Util  Compute M. |\n",
-            "|                                         |                      |               MIG M. |\n",
-            "|=========================================+======================+======================|\n",
-            "|   0  Tesla T4                       Off | 00000000:00:04.0 Off |                    0 |\n",
-            "| N/A   54C    P0              75W /  70W |   2825MiB / 15360MiB |     74%      Default |\n",
-            "|                                         |                      |                  N/A |\n",
-            "+-----------------------------------------+----------------------+----------------------+\n",
-            "                                                                                         \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| Processes:                                                                            |\n",
-            "|  GPU   GI   CI        PID   Type   Process name                            GPU Memory |\n",
-            "|        ID   ID                                                             Usage      |\n",
-            "|=======================================================================================|\n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "(21767, 1) (28480, 2)\n",
-            "CPU times: user 3.04 s, sys: 63.6 ms, total: 3.1 s\n",
-            "Wall time: 3.25 s\n"
-          ]
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "                               0        1        2         3         4\n",
+              "hops                           1        2        3         4         5\n",
+              "CPU hop chain time (s)   33.7597   50.877  228.473  291.1332  327.8891\n",
+              "GPU hop chain time (s)    0.3082   0.6515   2.9645    4.1146    4.7598\n",
+              "n_notation speedup      109.5356  78.0912  77.0694   70.7561   68.8877"
+            ],
+            "text/html": [
+              "\n",
+              "  <div id=\"df-590c3264-bd85-4c6f-aafc-919044461f9a\" class=\"colab-df-container\">\n",
+              "    <div>\n",
+              "<style scoped>\n",
+              "    .dataframe tbody tr th:only-of-type {\n",
+              "        vertical-align: middle;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe tbody tr th {\n",
+              "        vertical-align: top;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe thead th {\n",
+              "        text-align: right;\n",
+              "    }\n",
+              "</style>\n",
+              "<table border=\"1\" class=\"dataframe\">\n",
+              "  <thead>\n",
+              "    <tr style=\"text-align: right;\">\n",
+              "      <th></th>\n",
+              "      <th>0</th>\n",
+              "      <th>1</th>\n",
+              "      <th>2</th>\n",
+              "      <th>3</th>\n",
+              "      <th>4</th>\n",
+              "    </tr>\n",
+              "  </thead>\n",
+              "  <tbody>\n",
+              "    <tr>\n",
+              "      <th>hops</th>\n",
+              "      <td>1</td>\n",
+              "      <td>2</td>\n",
+              "      <td>3</td>\n",
+              "      <td>4</td>\n",
+              "      <td>5</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>CPU hop chain time (s)</th>\n",
+              "      <td>33.7597</td>\n",
+              "      <td>50.877</td>\n",
+              "      <td>228.473</td>\n",
+              "      <td>291.1332</td>\n",
+              "      <td>327.8891</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>GPU hop chain time (s)</th>\n",
+              "      <td>0.3082</td>\n",
+              "      <td>0.6515</td>\n",
+              "      <td>2.9645</td>\n",
+              "      <td>4.1146</td>\n",
+              "      <td>4.7598</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>n_notation speedup</th>\n",
+              "      <td>109.5356</td>\n",
+              "      <td>78.0912</td>\n",
+              "      <td>77.0694</td>\n",
+              "      <td>70.7561</td>\n",
+              "      <td>68.8877</td>\n",
+              "    </tr>\n",
+              "  </tbody>\n",
+              "</table>\n",
+              "</div>\n",
+              "    <div class=\"colab-df-buttons\">\n",
+              "\n",
+              "  <div class=\"colab-df-container\">\n",
+              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-590c3264-bd85-4c6f-aafc-919044461f9a')\"\n",
+              "            title=\"Convert this dataframe to an interactive table.\"\n",
+              "            style=\"display:none;\">\n",
+              "\n",
+              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
+              "    <path d=\"M120-120v-720h720v720H120Zm60-500h600v-160H180v160Zm220 220h160v-160H400v160Zm0 220h160v-160H400v160ZM180-400h160v-160H180v160Zm440 0h160v-160H620v160ZM180-180h160v-160H180v160Zm440 0h160v-160H620v160Z\"/>\n",
+              "  </svg>\n",
+              "    </button>\n",
+              "\n",
+              "  <style>\n",
+              "    .colab-df-container {\n",
+              "      display:flex;\n",
+              "      gap: 12px;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-convert {\n",
+              "      background-color: #E8F0FE;\n",
+              "      border: none;\n",
+              "      border-radius: 50%;\n",
+              "      cursor: pointer;\n",
+              "      display: none;\n",
+              "      fill: #1967D2;\n",
+              "      height: 32px;\n",
+              "      padding: 0 0 0 0;\n",
+              "      width: 32px;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-convert:hover {\n",
+              "      background-color: #E2EBFA;\n",
+              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
+              "      fill: #174EA6;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-buttons div {\n",
+              "      margin-bottom: 4px;\n",
+              "    }\n",
+              "\n",
+              "    [theme=dark] .colab-df-convert {\n",
+              "      background-color: #3B4455;\n",
+              "      fill: #D2E3FC;\n",
+              "    }\n",
+              "\n",
+              "    [theme=dark] .colab-df-convert:hover {\n",
+              "      background-color: #434B5C;\n",
+              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
+              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
+              "      fill: #FFFFFF;\n",
+              "    }\n",
+              "  </style>\n",
+              "\n",
+              "    <script>\n",
+              "      const buttonEl =\n",
+              "        document.querySelector('#df-590c3264-bd85-4c6f-aafc-919044461f9a button.colab-df-convert');\n",
+              "      buttonEl.style.display =\n",
+              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
+              "\n",
+              "      async function convertToInteractive(key) {\n",
+              "        const element = document.querySelector('#df-590c3264-bd85-4c6f-aafc-919044461f9a');\n",
+              "        const dataTable =\n",
+              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
+              "                                                    [key], {});\n",
+              "        if (!dataTable) return;\n",
+              "\n",
+              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
+              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
+              "          + ' to learn more about interactive tables.';\n",
+              "        element.innerHTML = '';\n",
+              "        dataTable['output_type'] = 'display_data';\n",
+              "        await google.colab.output.renderOutput(dataTable, element);\n",
+              "        const docLink = document.createElement('div');\n",
+              "        docLink.innerHTML = docLinkHtml;\n",
+              "        element.appendChild(docLink);\n",
+              "      }\n",
+              "    </script>\n",
+              "  </div>\n",
+              "\n",
+              "\n",
+              "<div id=\"df-ba3d9f1f-4569-493c-b04d-ca1c3fbc9b46\">\n",
+              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-ba3d9f1f-4569-493c-b04d-ca1c3fbc9b46')\"\n",
+              "            title=\"Suggest charts\"\n",
+              "            style=\"display:none;\">\n",
+              "\n",
+              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
+              "     width=\"24px\">\n",
+              "    <g>\n",
+              "        <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
+              "    </g>\n",
+              "</svg>\n",
+              "  </button>\n",
+              "\n",
+              "<style>\n",
+              "  .colab-df-quickchart {\n",
+              "      --bg-color: #E8F0FE;\n",
+              "      --fill-color: #1967D2;\n",
+              "      --hover-bg-color: #E2EBFA;\n",
+              "      --hover-fill-color: #174EA6;\n",
+              "      --disabled-fill-color: #AAA;\n",
+              "      --disabled-bg-color: #DDD;\n",
+              "  }\n",
+              "\n",
+              "  [theme=dark] .colab-df-quickchart {\n",
+              "      --bg-color: #3B4455;\n",
+              "      --fill-color: #D2E3FC;\n",
+              "      --hover-bg-color: #434B5C;\n",
+              "      --hover-fill-color: #FFFFFF;\n",
+              "      --disabled-bg-color: #3B4455;\n",
+              "      --disabled-fill-color: #666;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart {\n",
+              "    background-color: var(--bg-color);\n",
+              "    border: none;\n",
+              "    border-radius: 50%;\n",
+              "    cursor: pointer;\n",
+              "    display: none;\n",
+              "    fill: var(--fill-color);\n",
+              "    height: 32px;\n",
+              "    padding: 0;\n",
+              "    width: 32px;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart:hover {\n",
+              "    background-color: var(--hover-bg-color);\n",
+              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
+              "    fill: var(--button-hover-fill-color);\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart-complete:disabled,\n",
+              "  .colab-df-quickchart-complete:disabled:hover {\n",
+              "    background-color: var(--disabled-bg-color);\n",
+              "    fill: var(--disabled-fill-color);\n",
+              "    box-shadow: none;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-spinner {\n",
+              "    border: 2px solid var(--fill-color);\n",
+              "    border-color: transparent;\n",
+              "    border-bottom-color: var(--fill-color);\n",
+              "    animation:\n",
+              "      spin 1s steps(1) infinite;\n",
+              "  }\n",
+              "\n",
+              "  @keyframes spin {\n",
+              "    0% {\n",
+              "      border-color: transparent;\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "      border-left-color: var(--fill-color);\n",
+              "    }\n",
+              "    20% {\n",
+              "      border-color: transparent;\n",
+              "      border-left-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "    }\n",
+              "    30% {\n",
+              "      border-color: transparent;\n",
+              "      border-left-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "      border-right-color: var(--fill-color);\n",
+              "    }\n",
+              "    40% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "    }\n",
+              "    60% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "    }\n",
+              "    80% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "    }\n",
+              "    90% {\n",
+              "      border-color: transparent;\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "    }\n",
+              "  }\n",
+              "</style>\n",
+              "\n",
+              "  <script>\n",
+              "    async function quickchart(key) {\n",
+              "      const quickchartButtonEl =\n",
+              "        document.querySelector('#' + key + ' button');\n",
+              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
+              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
+              "      try {\n",
+              "        const charts = await google.colab.kernel.invokeFunction(\n",
+              "            'suggestCharts', [key], {});\n",
+              "      } catch (error) {\n",
+              "        console.error('Error during call to suggestCharts:', error);\n",
+              "      }\n",
+              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
+              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
+              "    }\n",
+              "    (() => {\n",
+              "      let quickchartButtonEl =\n",
+              "        document.querySelector('#df-ba3d9f1f-4569-493c-b04d-ca1c3fbc9b46 button');\n",
+              "      quickchartButtonEl.style.display =\n",
+              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
+              "    })();\n",
+              "  </script>\n",
+              "</div>\n",
+              "\n",
+              "    </div>\n",
+              "  </div>\n"
+            ],
+            "application/vnd.google.colaboratory.intrinsic+json": {
+              "type": "dataframe",
+              "summary": "{\n  \"name\": \"(results_df\",\n  \"rows\": 4,\n  \"fields\": [\n    {\n      \"column\": 0,\n      \"properties\": {\n        \"dtype\": \"date\",\n        \"min\": 0.3082,\n        \"max\": 109.5356,\n        \"num_unique_values\": 4,\n        \"samples\": [\n          33.7597,\n          109.5356,\n          1\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": 1,\n      \"properties\": {\n        \"dtype\": \"date\",\n        \"min\": 0.6515,\n        \"max\": 78.0912,\n        \"num_unique_values\": 4,\n        \"samples\": [\n          50.877,\n          78.0912,\n          2\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": 2,\n      \"properties\": {\n        \"dtype\": \"date\",\n        \"min\": 2.9645,\n        \"max\": 228.473,\n        \"num_unique_values\": 4,\n        \"samples\": [\n          228.473,\n          77.0694,\n          3\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": 3,\n      \"properties\": {\n        \"dtype\": \"date\",\n        \"min\": 4,\n        \"max\": 291.1332,\n        \"num_unique_values\": 4,\n        \"samples\": [\n          291.1332,\n          70.7561,\n          4\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": 4,\n      \"properties\": {\n        \"dtype\": \"date\",\n        \"min\": 4.7598,\n        \"max\": 327.8891,\n        \"num_unique_values\": 4,\n        \"samples\": [\n          327.8891,\n          68.8877,\n          5\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
+            }
+          },
+          "metadata": {},
+          "execution_count": 28
         }
       ]
     },
     {
-      "cell_type": "code",
+      "cell_type": "markdown",
       "source": [
-        "%%time\n",
-        "start_nodes = cudf.DataFrame({'id': [1]})\n",
-        "co_gdf = co_g.nodes(lambda g: cudf.DataFrame(g._nodes)).edges(lambda g: cudf.DataFrame(g._edges))\n",
-        "! nvidia-smi\n",
-        "for i in range(10):\n",
-        "  g2 = co_gdf.hop(\n",
-        "      nodes=start_nodes,\n",
-        "      direction='forward',\n",
-        "      hops=4)\n",
-        "! nvidia-smi\n",
-        "print(g2._nodes.shape, g2._edges.shape)\n",
-        "del start_nodes\n",
-        "del co_gdf\n",
-        "del g2"
+        "and similarly for these hop operations -- **100x** speed increases"
       ],
       "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "oNLZGjwInc85",
-        "outputId": "534097cf-4022-48cc-9419-a00c135f69e1"
-      },
-      "execution_count": 19,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "Tue Dec 26 00:56:53 2023       \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| NVIDIA-SMI 535.104.05             Driver Version: 535.104.05   CUDA Version: 12.2     |\n",
-            "|-----------------------------------------+----------------------+----------------------+\n",
-            "| GPU  Name                 Persistence-M | Bus-Id        Disp.A | Volatile Uncorr. ECC |\n",
-            "| Fan  Temp   Perf          Pwr:Usage/Cap |         Memory-Usage | GPU-Util  Compute M. |\n",
-            "|                                         |                      |               MIG M. |\n",
-            "|=========================================+======================+======================|\n",
-            "|   0  Tesla T4                       Off | 00000000:00:04.0 Off |                    0 |\n",
-            "| N/A   54C    P0              36W /  70W |   1927MiB / 15360MiB |     54%      Default |\n",
-            "|                                         |                      |                  N/A |\n",
-            "+-----------------------------------------+----------------------+----------------------+\n",
-            "                                                                                         \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| Processes:                                                                            |\n",
-            "|  GPU   GI   CI        PID   Type   Process name                            GPU Memory |\n",
-            "|        ID   ID                                                             Usage      |\n",
-            "|=======================================================================================|\n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "Tue Dec 26 00:56:58 2023       \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| NVIDIA-SMI 535.104.05             Driver Version: 535.104.05   CUDA Version: 12.2     |\n",
-            "|-----------------------------------------+----------------------+----------------------+\n",
-            "| GPU  Name                 Persistence-M | Bus-Id        Disp.A | Volatile Uncorr. ECC |\n",
-            "| Fan  Temp   Perf          Pwr:Usage/Cap |         Memory-Usage | GPU-Util  Compute M. |\n",
-            "|                                         |                      |               MIG M. |\n",
-            "|=========================================+======================+======================|\n",
-            "|   0  Tesla T4                       Off | 00000000:00:04.0 Off |                    0 |\n",
-            "| N/A   56C    P0              38W /  70W |   2907MiB / 15360MiB |     89%      Default |\n",
-            "|                                         |                      |                  N/A |\n",
-            "+-----------------------------------------+----------------------+----------------------+\n",
-            "                                                                                         \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| Processes:                                                                            |\n",
-            "|  GPU   GI   CI        PID   Type   Process name                            GPU Memory |\n",
-            "|        ID   ID                                                             Usage      |\n",
-            "|=======================================================================================|\n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "(718640, 1) (2210961, 2)\n",
-            "CPU times: user 4.58 s, sys: 309 ms, total: 4.89 s\n",
-            "Wall time: 5.02 s\n"
-          ]
-        }
-      ]
+        "id": "80bs6Y5pBWb2"
+      }
     },
     {
       "cell_type": "code",
       "source": [
-        "%%time\n",
-        "start_nodes = cudf.DataFrame({'id': [1]})\n",
-        "co_gdf = co_g.nodes(lambda g: cudf.DataFrame(g._nodes)).edges(lambda g: cudf.DataFrame(g._edges))\n",
-        "! nvidia-smi\n",
-        "for i in range(10):\n",
-        "  g2 = co_gdf.hop(\n",
-        "      nodes=start_nodes,\n",
-        "      direction='forward',\n",
-        "      hops=5)\n",
-        "! nvidia-smi\n",
-        "print(g2._nodes.shape, g2._edges.shape)\n",
-        "del start_nodes\n",
-        "del co_gdf\n",
-        "del g2"
+        "results_df = pd.DataFrame(columns=['hops', 'CPU hop chain time (s)', 'GPU hop chain time (s)', 'n_notation speedup'])\n",
+        "\n",
+        "\n",
+        "for n_hop in [1,2,3,4,5]:\n",
+        "    start_nodes = pd.DataFrame({gg._node: ['116374117927631468606']})\n",
+        "    start0 = time.time()\n",
+        "    for i in range(1):\n",
+        "      g2 = gg.hop(\n",
+        "          nodes=start_nodes,\n",
+        "          direction='forward',\n",
+        "          hops=n_hop)\n",
+        "    end0 = time.time()\n",
+        "    T0 = end0-start0\n",
+        "    start_nodes = cudf.DataFrame({gg._node: ['116374117927631468606']})\n",
+        "    gg_gdf = gg.nodes(cudf.from_pandas(gg._nodes)).edges(cudf.from_pandas(gg._edges))\n",
+        "    start1 = time.time()\n",
+        "    for i in range(1):\n",
+        "      g2 = gg_gdf.hop(\n",
+        "          nodes=start_nodes,\n",
+        "          direction='forward',\n",
+        "          hops=n_hop)\n",
+        "    end1 = time.time()\n",
+        "\n",
+        "    del start_nodes\n",
+        "    del gg_gdf\n",
+        "    del g2\n",
+        "    T1 = end1-start1\n",
+        "\n",
+        "    new_row = pd.DataFrame({\n",
+        "        'hops': [n_hop],\n",
+        "        'CPU hop chain time (s)': [np.round(T0, 4)],\n",
+        "        'GPU hop chain time (s)': [np.round(T1, 4)],\n",
+        "        'n_notation speedup': [np.round(T0 / T1, 4)]\n",
+        "    })\n",
+        "\n",
+        "    results_df = pd.concat([results_df, new_row], ignore_index=True)\n",
+        "\n",
+        "(results_df.T)"
       ],
       "metadata": {
         "colab": {
-          "base_uri": "https://localhost:8080/"
+          "base_uri": "https://localhost:8080/",
+          "height": 175
         },
-        "id": "ePqaeujMneX8",
-        "outputId": "ffd88fff-016e-4ac0-ecb9-fa06baca60f8"
+        "id": "N2-gDFod9vc3",
+        "outputId": "907da762-fae2-4caa-cdd2-e78e13b2f635"
       },
-      "execution_count": 20,
+      "execution_count": 29,
       "outputs": [
         {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "Tue Dec 26 00:56:58 2023       \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| NVIDIA-SMI 535.104.05             Driver Version: 535.104.05   CUDA Version: 12.2     |\n",
-            "|-----------------------------------------+----------------------+----------------------+\n",
-            "| GPU  Name                 Persistence-M | Bus-Id        Disp.A | Volatile Uncorr. ECC |\n",
-            "| Fan  Temp   Perf          Pwr:Usage/Cap |         Memory-Usage | GPU-Util  Compute M. |\n",
-            "|                                         |                      |               MIG M. |\n",
-            "|=========================================+======================+======================|\n",
-            "|   0  Tesla T4                       Off | 00000000:00:04.0 Off |                    0 |\n",
-            "| N/A   55C    P0              37W /  70W |   1925MiB / 15360MiB |     59%      Default |\n",
-            "|                                         |                      |                  N/A |\n",
-            "+-----------------------------------------+----------------------+----------------------+\n",
-            "                                                                                         \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| Processes:                                                                            |\n",
-            "|  GPU   GI   CI        PID   Type   Process name                            GPU Memory |\n",
-            "|        ID   ID                                                             Usage      |\n",
-            "|=======================================================================================|\n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "Tue Dec 26 00:57:10 2023       \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| NVIDIA-SMI 535.104.05             Driver Version: 535.104.05   CUDA Version: 12.2     |\n",
-            "|-----------------------------------------+----------------------+----------------------+\n",
-            "| GPU  Name                 Persistence-M | Bus-Id        Disp.A | Volatile Uncorr. ECC |\n",
-            "| Fan  Temp   Perf          Pwr:Usage/Cap |         Memory-Usage | GPU-Util  Compute M. |\n",
-            "|                                         |                      |               MIG M. |\n",
-            "|=========================================+======================+======================|\n",
-            "|   0  Tesla T4                       Off | 00000000:00:04.0 Off |                    0 |\n",
-            "| N/A   60C    P0              48W /  70W |   4325MiB / 15360MiB |     99%      Default |\n",
-            "|                                         |                      |                  N/A |\n",
-            "+-----------------------------------------+----------------------+----------------------+\n",
-            "                                                                                         \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| Processes:                                                                            |\n",
-            "|  GPU   GI   CI        PID   Type   Process name                            GPU Memory |\n",
-            "|        ID   ID                                                             Usage      |\n",
-            "|=======================================================================================|\n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "(3041556, 1) (47622917, 2)\n",
-            "CPU times: user 10.8 s, sys: 1.29 s, total: 12.1 s\n",
-            "Wall time: 12 s\n"
-          ]
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "                               0         1        2        3         4\n",
+              "hops                           1         2        3        4         5\n",
+              "CPU hop chain time (s)   19.6594   33.2538  64.8384  98.9693  147.4526\n",
+              "GPU hop chain time (s)     0.116    0.2583   0.8252   1.3544    1.9375\n",
+              "n_notation speedup      169.4189  128.7532  78.5772   73.071    76.103"
+            ],
+            "text/html": [
+              "\n",
+              "  <div id=\"df-429deec3-cdf5-46a1-a230-330fac6eb410\" class=\"colab-df-container\">\n",
+              "    <div>\n",
+              "<style scoped>\n",
+              "    .dataframe tbody tr th:only-of-type {\n",
+              "        vertical-align: middle;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe tbody tr th {\n",
+              "        vertical-align: top;\n",
+              "    }\n",
+              "\n",
+              "    .dataframe thead th {\n",
+              "        text-align: right;\n",
+              "    }\n",
+              "</style>\n",
+              "<table border=\"1\" class=\"dataframe\">\n",
+              "  <thead>\n",
+              "    <tr style=\"text-align: right;\">\n",
+              "      <th></th>\n",
+              "      <th>0</th>\n",
+              "      <th>1</th>\n",
+              "      <th>2</th>\n",
+              "      <th>3</th>\n",
+              "      <th>4</th>\n",
+              "    </tr>\n",
+              "  </thead>\n",
+              "  <tbody>\n",
+              "    <tr>\n",
+              "      <th>hops</th>\n",
+              "      <td>1</td>\n",
+              "      <td>2</td>\n",
+              "      <td>3</td>\n",
+              "      <td>4</td>\n",
+              "      <td>5</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>CPU hop chain time (s)</th>\n",
+              "      <td>19.6594</td>\n",
+              "      <td>33.2538</td>\n",
+              "      <td>64.8384</td>\n",
+              "      <td>98.9693</td>\n",
+              "      <td>147.4526</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>GPU hop chain time (s)</th>\n",
+              "      <td>0.116</td>\n",
+              "      <td>0.2583</td>\n",
+              "      <td>0.8252</td>\n",
+              "      <td>1.3544</td>\n",
+              "      <td>1.9375</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <th>n_notation speedup</th>\n",
+              "      <td>169.4189</td>\n",
+              "      <td>128.7532</td>\n",
+              "      <td>78.5772</td>\n",
+              "      <td>73.071</td>\n",
+              "      <td>76.103</td>\n",
+              "    </tr>\n",
+              "  </tbody>\n",
+              "</table>\n",
+              "</div>\n",
+              "    <div class=\"colab-df-buttons\">\n",
+              "\n",
+              "  <div class=\"colab-df-container\">\n",
+              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-429deec3-cdf5-46a1-a230-330fac6eb410')\"\n",
+              "            title=\"Convert this dataframe to an interactive table.\"\n",
+              "            style=\"display:none;\">\n",
+              "\n",
+              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
+              "    <path d=\"M120-120v-720h720v720H120Zm60-500h600v-160H180v160Zm220 220h160v-160H400v160Zm0 220h160v-160H400v160ZM180-400h160v-160H180v160Zm440 0h160v-160H620v160ZM180-180h160v-160H180v160Zm440 0h160v-160H620v160Z\"/>\n",
+              "  </svg>\n",
+              "    </button>\n",
+              "\n",
+              "  <style>\n",
+              "    .colab-df-container {\n",
+              "      display:flex;\n",
+              "      gap: 12px;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-convert {\n",
+              "      background-color: #E8F0FE;\n",
+              "      border: none;\n",
+              "      border-radius: 50%;\n",
+              "      cursor: pointer;\n",
+              "      display: none;\n",
+              "      fill: #1967D2;\n",
+              "      height: 32px;\n",
+              "      padding: 0 0 0 0;\n",
+              "      width: 32px;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-convert:hover {\n",
+              "      background-color: #E2EBFA;\n",
+              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
+              "      fill: #174EA6;\n",
+              "    }\n",
+              "\n",
+              "    .colab-df-buttons div {\n",
+              "      margin-bottom: 4px;\n",
+              "    }\n",
+              "\n",
+              "    [theme=dark] .colab-df-convert {\n",
+              "      background-color: #3B4455;\n",
+              "      fill: #D2E3FC;\n",
+              "    }\n",
+              "\n",
+              "    [theme=dark] .colab-df-convert:hover {\n",
+              "      background-color: #434B5C;\n",
+              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
+              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
+              "      fill: #FFFFFF;\n",
+              "    }\n",
+              "  </style>\n",
+              "\n",
+              "    <script>\n",
+              "      const buttonEl =\n",
+              "        document.querySelector('#df-429deec3-cdf5-46a1-a230-330fac6eb410 button.colab-df-convert');\n",
+              "      buttonEl.style.display =\n",
+              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
+              "\n",
+              "      async function convertToInteractive(key) {\n",
+              "        const element = document.querySelector('#df-429deec3-cdf5-46a1-a230-330fac6eb410');\n",
+              "        const dataTable =\n",
+              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
+              "                                                    [key], {});\n",
+              "        if (!dataTable) return;\n",
+              "\n",
+              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
+              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
+              "          + ' to learn more about interactive tables.';\n",
+              "        element.innerHTML = '';\n",
+              "        dataTable['output_type'] = 'display_data';\n",
+              "        await google.colab.output.renderOutput(dataTable, element);\n",
+              "        const docLink = document.createElement('div');\n",
+              "        docLink.innerHTML = docLinkHtml;\n",
+              "        element.appendChild(docLink);\n",
+              "      }\n",
+              "    </script>\n",
+              "  </div>\n",
+              "\n",
+              "\n",
+              "<div id=\"df-4d398349-e7b1-40b1-99db-ed24eefadb6f\">\n",
+              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-4d398349-e7b1-40b1-99db-ed24eefadb6f')\"\n",
+              "            title=\"Suggest charts\"\n",
+              "            style=\"display:none;\">\n",
+              "\n",
+              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
+              "     width=\"24px\">\n",
+              "    <g>\n",
+              "        <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
+              "    </g>\n",
+              "</svg>\n",
+              "  </button>\n",
+              "\n",
+              "<style>\n",
+              "  .colab-df-quickchart {\n",
+              "      --bg-color: #E8F0FE;\n",
+              "      --fill-color: #1967D2;\n",
+              "      --hover-bg-color: #E2EBFA;\n",
+              "      --hover-fill-color: #174EA6;\n",
+              "      --disabled-fill-color: #AAA;\n",
+              "      --disabled-bg-color: #DDD;\n",
+              "  }\n",
+              "\n",
+              "  [theme=dark] .colab-df-quickchart {\n",
+              "      --bg-color: #3B4455;\n",
+              "      --fill-color: #D2E3FC;\n",
+              "      --hover-bg-color: #434B5C;\n",
+              "      --hover-fill-color: #FFFFFF;\n",
+              "      --disabled-bg-color: #3B4455;\n",
+              "      --disabled-fill-color: #666;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart {\n",
+              "    background-color: var(--bg-color);\n",
+              "    border: none;\n",
+              "    border-radius: 50%;\n",
+              "    cursor: pointer;\n",
+              "    display: none;\n",
+              "    fill: var(--fill-color);\n",
+              "    height: 32px;\n",
+              "    padding: 0;\n",
+              "    width: 32px;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart:hover {\n",
+              "    background-color: var(--hover-bg-color);\n",
+              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
+              "    fill: var(--button-hover-fill-color);\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-quickchart-complete:disabled,\n",
+              "  .colab-df-quickchart-complete:disabled:hover {\n",
+              "    background-color: var(--disabled-bg-color);\n",
+              "    fill: var(--disabled-fill-color);\n",
+              "    box-shadow: none;\n",
+              "  }\n",
+              "\n",
+              "  .colab-df-spinner {\n",
+              "    border: 2px solid var(--fill-color);\n",
+              "    border-color: transparent;\n",
+              "    border-bottom-color: var(--fill-color);\n",
+              "    animation:\n",
+              "      spin 1s steps(1) infinite;\n",
+              "  }\n",
+              "\n",
+              "  @keyframes spin {\n",
+              "    0% {\n",
+              "      border-color: transparent;\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "      border-left-color: var(--fill-color);\n",
+              "    }\n",
+              "    20% {\n",
+              "      border-color: transparent;\n",
+              "      border-left-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "    }\n",
+              "    30% {\n",
+              "      border-color: transparent;\n",
+              "      border-left-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "      border-right-color: var(--fill-color);\n",
+              "    }\n",
+              "    40% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "      border-top-color: var(--fill-color);\n",
+              "    }\n",
+              "    60% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "    }\n",
+              "    80% {\n",
+              "      border-color: transparent;\n",
+              "      border-right-color: var(--fill-color);\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "    }\n",
+              "    90% {\n",
+              "      border-color: transparent;\n",
+              "      border-bottom-color: var(--fill-color);\n",
+              "    }\n",
+              "  }\n",
+              "</style>\n",
+              "\n",
+              "  <script>\n",
+              "    async function quickchart(key) {\n",
+              "      const quickchartButtonEl =\n",
+              "        document.querySelector('#' + key + ' button');\n",
+              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
+              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
+              "      try {\n",
+              "        const charts = await google.colab.kernel.invokeFunction(\n",
+              "            'suggestCharts', [key], {});\n",
+              "      } catch (error) {\n",
+              "        console.error('Error during call to suggestCharts:', error);\n",
+              "      }\n",
+              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
+              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
+              "    }\n",
+              "    (() => {\n",
+              "      let quickchartButtonEl =\n",
+              "        document.querySelector('#df-4d398349-e7b1-40b1-99db-ed24eefadb6f button');\n",
+              "      quickchartButtonEl.style.display =\n",
+              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
+              "    })();\n",
+              "  </script>\n",
+              "</div>\n",
+              "\n",
+              "    </div>\n",
+              "  </div>\n"
+            ],
+            "application/vnd.google.colaboratory.intrinsic+json": {
+              "type": "dataframe",
+              "summary": "{\n  \"name\": \"(results_df\",\n  \"rows\": 4,\n  \"fields\": [\n    {\n      \"column\": 0,\n      \"properties\": {\n        \"dtype\": \"date\",\n        \"min\": 0.116,\n        \"max\": 169.4189,\n        \"num_unique_values\": 4,\n        \"samples\": [\n          19.6594,\n          169.4189,\n          1\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": 1,\n      \"properties\": {\n        \"dtype\": \"date\",\n        \"min\": 0.2583,\n        \"max\": 128.7532,\n        \"num_unique_values\": 4,\n        \"samples\": [\n          33.2538,\n          128.7532,\n          2\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": 2,\n      \"properties\": {\n        \"dtype\": \"date\",\n        \"min\": 0.8252,\n        \"max\": 78.5772,\n        \"num_unique_values\": 4,\n        \"samples\": [\n          64.8384,\n          78.5772,\n          3\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": 3,\n      \"properties\": {\n        \"dtype\": \"date\",\n        \"min\": 1.3544,\n        \"max\": 98.9693,\n        \"num_unique_values\": 4,\n        \"samples\": [\n          98.9693,\n          73.071,\n          4\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": 4,\n      \"properties\": {\n        \"dtype\": \"date\",\n        \"min\": 1.9375,\n        \"max\": 147.4526,\n        \"num_unique_values\": 4,\n        \"samples\": [\n          147.4526,\n          76.103,\n          5\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
+            }
+          },
+          "metadata": {},
+          "execution_count": 29
         }
       ]
+    }
+  ],
+  "metadata": {
+    "accelerator": "GPU",
+    "colab": {
+      "gpuType": "T4",
+      "provenance": []
     },
-    {
-      "cell_type": "code",
-      "source": [
-        "%%time\n",
-        "start_nodes = cudf.DataFrame({'id': [1]})\n",
-        "co_gdf = co_g.nodes(lambda g: cudf.DataFrame(g._nodes)).edges(lambda g: cudf.DataFrame(g._edges))\n",
-        "! nvidia-smi\n",
-        "for i in range(10):\n",
-        "  g2 = co_gdf.hop(\n",
-        "      nodes=start_nodes,\n",
-        "      direction='forward',\n",
-        "      hops=6)\n",
-        "! nvidia-smi\n",
-        "print(g2._nodes.shape, g2._edges.shape)\n",
-        "del start_nodes\n",
-        "del co_gdf\n",
-        "del g2"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "PTBkoIVHnfzK",
-        "outputId": "5615ecd7-47ea-46ab-fd36-13bce4b3c787"
-      },
-      "execution_count": 21,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "Tue Dec 26 00:57:10 2023       \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| NVIDIA-SMI 535.104.05             Driver Version: 535.104.05   CUDA Version: 12.2     |\n",
-            "|-----------------------------------------+----------------------+----------------------+\n",
-            "| GPU  Name                 Persistence-M | Bus-Id        Disp.A | Volatile Uncorr. ECC |\n",
-            "| Fan  Temp   Perf          Pwr:Usage/Cap |         Memory-Usage | GPU-Util  Compute M. |\n",
-            "|                                         |                      |               MIG M. |\n",
-            "|=========================================+======================+======================|\n",
-            "|   0  Tesla T4                       Off | 00000000:00:04.0 Off |                    0 |\n",
-            "| N/A   59C    P0              38W /  70W |   1925MiB / 15360MiB |     44%      Default |\n",
-            "|                                         |                      |                  N/A |\n",
-            "+-----------------------------------------+----------------------+----------------------+\n",
-            "                                                                                         \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| Processes:                                                                            |\n",
-            "|  GPU   GI   CI        PID   Type   Process name                            GPU Memory |\n",
-            "|        ID   ID                                                             Usage      |\n",
-            "|=======================================================================================|\n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "Tue Dec 26 00:57:38 2023       \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| NVIDIA-SMI 535.104.05             Driver Version: 535.104.05   CUDA Version: 12.2     |\n",
-            "|-----------------------------------------+----------------------+----------------------+\n",
-            "| GPU  Name                 Persistence-M | Bus-Id        Disp.A | Volatile Uncorr. ECC |\n",
-            "| Fan  Temp   Perf          Pwr:Usage/Cap |         Memory-Usage | GPU-Util  Compute M. |\n",
-            "|                                         |                      |               MIG M. |\n",
-            "|=========================================+======================+======================|\n",
-            "|   0  Tesla T4                       Off | 00000000:00:04.0 Off |                    0 |\n",
-            "| N/A   68C    P0              55W /  70W |   6445MiB / 15360MiB |     95%      Default |\n",
-            "|                                         |                      |                  N/A |\n",
-            "+-----------------------------------------+----------------------+----------------------+\n",
-            "                                                                                         \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| Processes:                                                                            |\n",
-            "|  GPU   GI   CI        PID   Type   Process name                            GPU Memory |\n",
-            "|        ID   ID                                                             Usage      |\n",
-            "|=======================================================================================|\n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "(3071927, 1) (117032738, 2)\n",
-            "CPU times: user 23.5 s, sys: 2.68 s, total: 26.2 s\n",
-            "Wall time: 28.2 s\n"
-          ]
-        }
-      ]
+    "kernelspec": {
+      "display_name": "Python 3",
+      "name": "python3"
     },
-    {
-      "cell_type": "code",
-      "source": [],
-      "metadata": {
-        "id": "Ygc2nrkznlCu"
-      },
-      "execution_count": null,
-      "outputs": []
+    "language_info": {
+      "name": "python"
     }
-  ]
+  },
+  "nbformat": 4,
+  "nbformat_minor": 0
 }
\ No newline at end of file
diff --git a/demos/gfql/gfql_cpv_gpu_enchmark.ipynb b/demos/gfql/gfql_cpv_gpu_enchmark.ipynb
deleted file mode 100644
index 9860cc105e..0000000000
--- a/demos/gfql/gfql_cpv_gpu_enchmark.ipynb
+++ /dev/null
@@ -1,2976 +0,0 @@
-{
-  "cells": [
-    {
-      "cell_type": "markdown",
-      "metadata": {
-        "id": "view-in-github",
-        "colab_type": "text"
-      },
-      "source": [
-        "<a href=\"https://colab.research.google.com/github/dcolinmorgan/grph/blob/main/clean_gfql_cpu_gpu_benchmark.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
-      ]
-    },
-    {
-      "cell_type": "markdown",
-      "metadata": {
-        "id": "GZxoiU8sQDk_"
-      },
-      "source": [
-        "# GFQL CPU, GPU Benchmark\n",
-        "\n",
-        "This notebook examines GFQL property graph query performance on 1-8 hop queries using CPU + GPU modes on various real-world 100K - 100M edge graphs. The data comes from a variety of popular social networks. The single-threaded CPU mode benefits from GFQL's novel dataframe engine, and the GPU mode further adds single-GPU acceleration. Both the `chain()` and `hop()` methods are examined.\n",
-        "\n",
-        "The benchmark does not examine bigger-than-memory and distributed scenarios. The provided results here are from running on a free Google Colab T4 runtime, with a 2.2GHz Intel CPU (12 GB CPU RAM) and T4 Nvidia GPU (16 GB GPU RAM).\n",
-        "\n",
-        "## Data\n",
-        "From [SNAP](https://snap.stanford.edu/data/)\n",
-        "\n",
-        "| Network | Nodes     | Edges        |\n",
-        "|-------------|-----------|--------------|\n",
-        "| [**Facebook**](#fb)| 4,039     | 88,234       |\n",
-        "| [**Twitter**](#tw) | 81,306    | 2,420,766    |\n",
-        "| [**GPlus**](#gpl)   | 107,614   | 30,494,866   |\n",
-        "| [**Orkut**](#ork)   | 3,072,441 | 117,185,082  |\n",
-        "\n",
-        "## Results\n",
-        "\n",
-        "Definitions:\n",
-        "\n",
-        "* GTEPS: Giga (billion) edges traversed per second\n",
-        "\n",
-        "* T edges / \\$: Estimated trillion edges traversed for 1\\$ USD based on observed GTEPS and a 3yr AWS reservation (as of 12/2023)\n",
-        "\n",
-        "Tasks:\n",
-        "\n",
-        "1. `chain()` - includes complex pre/post processing\n",
-        "\n",
-        "  **Task**: `g.chain([n({'id': some_id}), e_forward(hops=some_n)])`\n",
-        "\n",
-        "\n",
-        "| **Dataset** | Max GPU Speedup      | CPU GTEPS   | GPU GTEPS   | T CPU edges / \\$ (t3.l) | T GPU edges / \\$ (g4dn.xl) |\n",
-        "|-------------|--------------|-------------|-------------|----------------------------|--------------------------------|\n",
-        "| [**Facebook**](#fb)| 1.1X  | 0.66 | 0.61 | 65.7                | 10.4                    |\n",
-        "| [**Twitter**](#tw) | 17.4X   | 0.17 | 2.81 | 16.7                | 48.1                    |\n",
-        "| [**GPlus**](#gpl)   | 43.8X  | 0.09 | 2.87 | 8.5                | 49.2                    |\n",
-        "| [**Orkut**](#ork)   | N/A            | N/A         | 12.15 | N/A                        | 208.3                    |\n",
-        "| **AVG** | 20.7X | 0.30 | 4.61 | 30.3 | 79.0\n",
-        "| **MAX** | 43.8X | 0.66 | 12.15 | 65.7 | 208.3\n",
-        "\n",
-        "\n",
-        "2. `hop()` - core property search primitive similar to BFS\n",
-        "\n",
-        "  **Task**: `g.hop(nodes=[some_id], direction='forward', hops=some_n)`\n",
-        "\n",
-        "\n",
-        "| **Dataset** | Max GPU Speedup | CPU GTEPS | GPU GTEPS | T CPU edges / \\$ (t3.l) | T GPU edges / \\$ (g4dn.xl) |\n",
-        "|-------------|-------------|-----------|-----------|--------------------|--------------------------------|\n",
-        "| [**Facebook**](#fb)| 3X          | 0.47      | 1.47     | 47.0        | 25.2                    |\n",
-        "| [**Twitter**](#tw) | 42X         | 0.50      | 10.51      | 50.2        | 180.2                    |\n",
-        "| [**GPlus**](#gpl)   | 21X         | 0.26      | 4.11       | 26.2        | 70.4                    |\n",
-        "| [**Orkut**](#ork)   | N/A         | N/A       | 41.50     | N/A                | 711.4                    |\n",
-        "| **AVG** | 22X | 0.41 | 14.4 | 41.1 | 246.8\n",
-        "| **MAX** | 42X | 0.50 | 41.50 | 50.2 | 711.4\n"
-      ]
-    },
-    {
-      "cell_type": "markdown",
-      "metadata": {
-        "id": "SAj8lhREEOwS"
-      },
-      "source": [
-        "## Optional: GPU setup - Google Colab"
-      ]
-    },
-    {
-      "cell_type": "markdown",
-      "metadata": {
-        "id": "4hrEEAAm7DTO"
-      },
-      "source": []
-    },
-    {
-      "cell_type": "code",
-      "execution_count": null,
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "W2MF6ZsjDv3B",
-        "outputId": "d09118ee-55d5-49cf-b950-d1e232aa4eb2"
-      },
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "Mon Feb 19 04:14:57 2024       \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| NVIDIA-SMI 535.104.05             Driver Version: 535.104.05   CUDA Version: 12.2     |\n",
-            "|-----------------------------------------+----------------------+----------------------+\n",
-            "| GPU  Name                 Persistence-M | Bus-Id        Disp.A | Volatile Uncorr. ECC |\n",
-            "| Fan  Temp   Perf          Pwr:Usage/Cap |         Memory-Usage | GPU-Util  Compute M. |\n",
-            "|                                         |                      |               MIG M. |\n",
-            "|=========================================+======================+======================|\n",
-            "|   0  Tesla T4                       Off | 00000000:00:04.0 Off |                    0 |\n",
-            "| N/A   39C    P8               9W /  70W |      0MiB / 15360MiB |      0%      Default |\n",
-            "|                                         |                      |                  N/A |\n",
-            "+-----------------------------------------+----------------------+----------------------+\n",
-            "                                                                                         \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| Processes:                                                                            |\n",
-            "|  GPU   GI   CI        PID   Type   Process name                            GPU Memory |\n",
-            "|        ID   ID                                                             Usage      |\n",
-            "|=======================================================================================|\n",
-            "|  No running processes found                                                           |\n",
-            "+---------------------------------------------------------------------------------------+\n"
-          ]
-        }
-      ],
-      "source": [
-        "# Report GPU used when GPU benchmarking\n",
-        "! nvidia-smi"
-      ]
-    },
-    {
-      "cell_type": "code",
-      "execution_count": null,
-      "metadata": {
-        "id": "Aikh0x4ID_wK"
-      },
-      "outputs": [],
-      "source": [
-        "# if in google colab\n",
-        "# !git clone https://github.com/rapidsai/rapidsai-csp-utils.git\n",
-        "# !python rapidsai-csp-utils/colab/pip-install.py\n",
-        "!pip install --extra-index-url=https://pypi.nvidia.com cuml-cu12 cudf-cu12 #==23.12.00 #cugraph-cu11 pylibraft_cu11 raft_dask_cu11 dask_cudf_cu11 pylibcugraph_cu11 pylibraft_cu11\n"
-      ]
-    },
-    {
-      "cell_type": "code",
-      "execution_count": null,
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/",
-          "height": 35
-        },
-        "id": "Lwekdei1dH3N",
-        "outputId": "a506b4fb-0dba-4e90-884e-df16cb19eebd"
-      },
-      "outputs": [
-        {
-          "output_type": "execute_result",
-          "data": {
-            "text/plain": [
-              "'24.02.01'"
-            ],
-            "application/vnd.google.colaboratory.intrinsic+json": {
-              "type": "string"
-            }
-          },
-          "metadata": {},
-          "execution_count": 2
-        }
-      ],
-      "source": [
-        "import cudf\n",
-        "cudf.__version__"
-      ]
-    },
-    {
-      "cell_type": "markdown",
-      "metadata": {
-        "id": "QQpsrtwBT7sa"
-      },
-      "source": [
-        "# 1. Install & configure"
-      ]
-    },
-    {
-      "cell_type": "code",
-      "execution_count": null,
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "cYjRbgkU9Sx8",
-        "outputId": "7d592f98-36af-4657-b8eb-80eeabd98e2f"
-      },
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m3.3/3.3 MB\u001b[0m \u001b[31m14.0 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
-            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m244.4/244.4 kB\u001b[0m \u001b[31m2.2 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
-            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m332.3/332.3 kB\u001b[0m \u001b[31m8.5 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
-            "\u001b[?25h"
-          ]
-        }
-      ],
-      "source": [
-        "#! pip install graphistry[igraph]\n",
-        "\n",
-        "!pip install -q igraph\n",
-        "!pip install -q graphistry\n"
-      ]
-    },
-    {
-      "cell_type": "markdown",
-      "metadata": {
-        "id": "Ff6Tt9DhkePl"
-      },
-      "source": [
-        "## Imports"
-      ]
-    },
-    {
-      "cell_type": "code",
-      "execution_count": null,
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/",
-          "height": 35
-        },
-        "id": "S5_y0CbLkjft",
-        "outputId": "909ff8a7-650e-4e65-aaf9-40f650d50145"
-      },
-      "outputs": [
-        {
-          "output_type": "execute_result",
-          "data": {
-            "text/plain": [
-              "'0.33.0'"
-            ],
-            "application/vnd.google.colaboratory.intrinsic+json": {
-              "type": "string"
-            }
-          },
-          "metadata": {},
-          "execution_count": 4
-        }
-      ],
-      "source": [
-        "import pandas as pd\n",
-        "\n",
-        "import graphistry, time\n",
-        "\n",
-        "from graphistry import (\n",
-        "\n",
-        "    # graph operators\n",
-        "    n, e_undirected, e_forward, e_reverse,\n",
-        "\n",
-        "    # attribute predicates\n",
-        "    is_in, ge, startswith, contains, match as match_re\n",
-        ")\n",
-        "graphistry.__version__"
-      ]
-    },
-    {
-      "cell_type": "code",
-      "execution_count": null,
-      "metadata": {
-        "id": "I7Fg75jsG4co"
-      },
-      "outputs": [],
-      "source": [
-        "import cudf"
-      ]
-    },
-    {
-      "cell_type": "code",
-      "execution_count": null,
-      "metadata": {
-        "id": "uLZKph2-a5M4"
-      },
-      "outputs": [],
-      "source": [
-        "#work around google colab shell encoding bugs\n",
-        "\n",
-        "import locale\n",
-        "locale.getpreferredencoding = lambda: \"UTF-8\""
-      ]
-    },
-    {
-      "cell_type": "markdown",
-      "metadata": {
-        "id": "eU9SyauNUHtR"
-      },
-      "source": [
-        "# 2. Perf benchmarks"
-      ]
-    },
-    {
-      "cell_type": "markdown",
-      "metadata": {
-        "id": "NA0Ym11fkB8j"
-      },
-      "source": [
-        "<a name=\"fb\"></a>\n",
-        "### Facebook: 88K edges"
-      ]
-    },
-    {
-      "cell_type": "code",
-      "execution_count": null,
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/",
-          "height": 224
-        },
-        "id": "vXuQogHekClJ",
-        "outputId": "de95808f-d1c9-4864-e8d9-b197f3d38413"
-      },
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "(88234, 2)\n"
-          ]
-        },
-        {
-          "output_type": "execute_result",
-          "data": {
-            "text/plain": [
-              "   s  d\n",
-              "0  0  1\n",
-              "1  0  2\n",
-              "2  0  3\n",
-              "3  0  4\n",
-              "4  0  5"
-            ],
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-              "    .dataframe tbody tr th:only-of-type {\n",
-              "        vertical-align: middle;\n",
-              "    }\n",
-              "\n",
-              "    .dataframe tbody tr th {\n",
-              "        vertical-align: top;\n",
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-              "\n",
-              "    .dataframe thead th {\n",
-              "        text-align: right;\n",
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-              "\n",
-              "    .colab-df-buttons div {\n",
-              "      margin-bottom: 4px;\n",
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-              "\n",
-              "    [theme=dark] .colab-df-convert {\n",
-              "      background-color: #3B4455;\n",
-              "      fill: #D2E3FC;\n",
-              "    }\n",
-              "\n",
-              "    [theme=dark] .colab-df-convert:hover {\n",
-              "      background-color: #434B5C;\n",
-              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
-              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
-              "      fill: #FFFFFF;\n",
-              "    }\n",
-              "  </style>\n",
-              "\n",
-              "    <script>\n",
-              "      const buttonEl =\n",
-              "        document.querySelector('#df-8d88e76b-5f6b-4c01-9976-d9cccf151e38 button.colab-df-convert');\n",
-              "      buttonEl.style.display =\n",
-              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
-              "\n",
-              "      async function convertToInteractive(key) {\n",
-              "        const element = document.querySelector('#df-8d88e76b-5f6b-4c01-9976-d9cccf151e38');\n",
-              "        const dataTable =\n",
-              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
-              "                                                    [key], {});\n",
-              "        if (!dataTable) return;\n",
-              "\n",
-              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
-              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
-              "          + ' to learn more about interactive tables.';\n",
-              "        element.innerHTML = '';\n",
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-              "\n",
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-              "      --bg-color: #3B4455;\n",
-              "      --fill-color: #D2E3FC;\n",
-              "      --hover-bg-color: #434B5C;\n",
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-              "      --disabled-bg-color: #3B4455;\n",
-              "      --disabled-fill-color: #666;\n",
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-              "\n",
-              "  .colab-df-quickchart {\n",
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-              "    border: none;\n",
-              "    border-radius: 50%;\n",
-              "    cursor: pointer;\n",
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-              "    width: 32px;\n",
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-              "\n",
-              "  .colab-df-quickchart:hover {\n",
-              "    background-color: var(--hover-bg-color);\n",
-              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
-              "    fill: var(--button-hover-fill-color);\n",
-              "  }\n",
-              "\n",
-              "  .colab-df-quickchart-complete:disabled,\n",
-              "  .colab-df-quickchart-complete:disabled:hover {\n",
-              "    background-color: var(--disabled-bg-color);\n",
-              "    fill: var(--disabled-fill-color);\n",
-              "    box-shadow: none;\n",
-              "  }\n",
-              "\n",
-              "  .colab-df-spinner {\n",
-              "    border: 2px solid var(--fill-color);\n",
-              "    border-color: transparent;\n",
-              "    border-bottom-color: var(--fill-color);\n",
-              "    animation:\n",
-              "      spin 1s steps(1) infinite;\n",
-              "  }\n",
-              "\n",
-              "  @keyframes spin {\n",
-              "    0% {\n",
-              "      border-color: transparent;\n",
-              "      border-bottom-color: var(--fill-color);\n",
-              "      border-left-color: var(--fill-color);\n",
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-              "      border-top-color: var(--fill-color);\n",
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-              "      border-top-color: var(--fill-color);\n",
-              "      border-right-color: var(--fill-color);\n",
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-              "      border-bottom-color: var(--fill-color);\n",
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-              "  }\n",
-              "</style>\n",
-              "\n",
-              "  <script>\n",
-              "    async function quickchart(key) {\n",
-              "      const quickchartButtonEl =\n",
-              "        document.querySelector('#' + key + ' button');\n",
-              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
-              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
-              "      try {\n",
-              "        const charts = await google.colab.kernel.invokeFunction(\n",
-              "            'suggestCharts', [key], {});\n",
-              "      } catch (error) {\n",
-              "        console.error('Error during call to suggestCharts:', error);\n",
-              "      }\n",
-              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
-              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
-              "    }\n",
-              "    (() => {\n",
-              "      let quickchartButtonEl =\n",
-              "        document.querySelector('#df-027a4397-12aa-439e-93da-49eac22ef242 button');\n",
-              "      quickchartButtonEl.style.display =\n",
-              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
-              "    })();\n",
-              "  </script>\n",
-              "</div>\n",
-              "    </div>\n",
-              "  </div>\n"
-            ],
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-              "variable_name": "df",
-              "summary": "{\n  \"name\": \"df\",\n  \"rows\": 88234,\n  \"fields\": [\n    {\n      \"column\": \"s\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 910,\n        \"min\": 0,\n        \"max\": 4031,\n        \"samples\": [\n          1624,\n          101,\n          377\n        ],\n        \"num_unique_values\": 3663,\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"d\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 893,\n        \"min\": 1,\n        \"max\": 4038,\n        \"samples\": [\n          2193,\n          150,\n          879\n        ],\n        \"num_unique_values\": 4037,\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
-            }
-          },
-          "metadata": {},
-          "execution_count": 7
-        }
-      ],
-      "source": [
-        "df = pd.read_csv('https://raw.githubusercontent.com/graphistry/pygraphistry/master/demos/data/facebook_combined.txt', sep=' ', names=['s', 'd'])\n",
-        "print(df.shape)\n",
-        "df.head(5)"
-      ]
-    },
-    {
-      "cell_type": "code",
-      "execution_count": null,
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/",
-          "height": 224
-        },
-        "id": "jEma7hvvkzkN",
-        "outputId": "98501752-d3df-4f5d-95b8-ff085a17894a"
-      },
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "(4039, 1) (88234, 2)\n"
-          ]
-        },
-        {
-          "output_type": "execute_result",
-          "data": {
-            "text/plain": [
-              "   id\n",
-              "0   0\n",
-              "1   1\n",
-              "2   2\n",
-              "3   3\n",
-              "4   4"
-            ],
-            "text/html": [
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-              "    <div>\n",
-              "<style scoped>\n",
-              "    .dataframe tbody tr th:only-of-type {\n",
-              "        vertical-align: middle;\n",
-              "    }\n",
-              "\n",
-              "    .dataframe tbody tr th {\n",
-              "        vertical-align: top;\n",
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-              "\n",
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-              "</style>\n",
-              "<table border=\"1\" class=\"dataframe\">\n",
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-              "      <td>3</td>\n",
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-              "      <td>4</td>\n",
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-              "    .colab-df-container {\n",
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-              "\n",
-              "    .colab-df-convert {\n",
-              "      background-color: #E8F0FE;\n",
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-              "      background-color: #E2EBFA;\n",
-              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
-              "      fill: #174EA6;\n",
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-              "\n",
-              "    .colab-df-buttons div {\n",
-              "      margin-bottom: 4px;\n",
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-              "\n",
-              "    [theme=dark] .colab-df-convert {\n",
-              "      background-color: #3B4455;\n",
-              "      fill: #D2E3FC;\n",
-              "    }\n",
-              "\n",
-              "    [theme=dark] .colab-df-convert:hover {\n",
-              "      background-color: #434B5C;\n",
-              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
-              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
-              "      fill: #FFFFFF;\n",
-              "    }\n",
-              "  </style>\n",
-              "\n",
-              "    <script>\n",
-              "      const buttonEl =\n",
-              "        document.querySelector('#df-a6096f22-dea0-424e-b5b9-6a8685fb8eec button.colab-df-convert');\n",
-              "      buttonEl.style.display =\n",
-              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
-              "\n",
-              "      async function convertToInteractive(key) {\n",
-              "        const element = document.querySelector('#df-a6096f22-dea0-424e-b5b9-6a8685fb8eec');\n",
-              "        const dataTable =\n",
-              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
-              "                                                    [key], {});\n",
-              "        if (!dataTable) return;\n",
-              "\n",
-              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
-              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
-              "          + ' to learn more about interactive tables.';\n",
-              "        element.innerHTML = '';\n",
-              "        dataTable['output_type'] = 'display_data';\n",
-              "        await google.colab.output.renderOutput(dataTable, element);\n",
-              "        const docLink = document.createElement('div');\n",
-              "        docLink.innerHTML = docLinkHtml;\n",
-              "        element.appendChild(docLink);\n",
-              "      }\n",
-              "    </script>\n",
-              "  </div>\n",
-              "\n",
-              "\n",
-              "<div id=\"df-857b100f-363e-41f4-8e2a-0628457e85bc\">\n",
-              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-857b100f-363e-41f4-8e2a-0628457e85bc')\"\n",
-              "            title=\"Suggest charts\"\n",
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-              "\n",
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-              "     width=\"24px\">\n",
-              "    <g>\n",
-              "        <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
-              "    </g>\n",
-              "</svg>\n",
-              "  </button>\n",
-              "\n",
-              "<style>\n",
-              "  .colab-df-quickchart {\n",
-              "      --bg-color: #E8F0FE;\n",
-              "      --fill-color: #1967D2;\n",
-              "      --hover-bg-color: #E2EBFA;\n",
-              "      --hover-fill-color: #174EA6;\n",
-              "      --disabled-fill-color: #AAA;\n",
-              "      --disabled-bg-color: #DDD;\n",
-              "  }\n",
-              "\n",
-              "  [theme=dark] .colab-df-quickchart {\n",
-              "      --bg-color: #3B4455;\n",
-              "      --fill-color: #D2E3FC;\n",
-              "      --hover-bg-color: #434B5C;\n",
-              "      --hover-fill-color: #FFFFFF;\n",
-              "      --disabled-bg-color: #3B4455;\n",
-              "      --disabled-fill-color: #666;\n",
-              "  }\n",
-              "\n",
-              "  .colab-df-quickchart {\n",
-              "    background-color: var(--bg-color);\n",
-              "    border: none;\n",
-              "    border-radius: 50%;\n",
-              "    cursor: pointer;\n",
-              "    display: none;\n",
-              "    fill: var(--fill-color);\n",
-              "    height: 32px;\n",
-              "    padding: 0;\n",
-              "    width: 32px;\n",
-              "  }\n",
-              "\n",
-              "  .colab-df-quickchart:hover {\n",
-              "    background-color: var(--hover-bg-color);\n",
-              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
-              "    fill: var(--button-hover-fill-color);\n",
-              "  }\n",
-              "\n",
-              "  .colab-df-quickchart-complete:disabled,\n",
-              "  .colab-df-quickchart-complete:disabled:hover {\n",
-              "    background-color: var(--disabled-bg-color);\n",
-              "    fill: var(--disabled-fill-color);\n",
-              "    box-shadow: none;\n",
-              "  }\n",
-              "\n",
-              "  .colab-df-spinner {\n",
-              "    border: 2px solid var(--fill-color);\n",
-              "    border-color: transparent;\n",
-              "    border-bottom-color: var(--fill-color);\n",
-              "    animation:\n",
-              "      spin 1s steps(1) infinite;\n",
-              "  }\n",
-              "\n",
-              "  @keyframes spin {\n",
-              "    0% {\n",
-              "      border-color: transparent;\n",
-              "      border-bottom-color: var(--fill-color);\n",
-              "      border-left-color: var(--fill-color);\n",
-              "    }\n",
-              "    20% {\n",
-              "      border-color: transparent;\n",
-              "      border-left-color: var(--fill-color);\n",
-              "      border-top-color: var(--fill-color);\n",
-              "    }\n",
-              "    30% {\n",
-              "      border-color: transparent;\n",
-              "      border-left-color: var(--fill-color);\n",
-              "      border-top-color: var(--fill-color);\n",
-              "      border-right-color: var(--fill-color);\n",
-              "    }\n",
-              "    40% {\n",
-              "      border-color: transparent;\n",
-              "      border-right-color: var(--fill-color);\n",
-              "      border-top-color: var(--fill-color);\n",
-              "    }\n",
-              "    60% {\n",
-              "      border-color: transparent;\n",
-              "      border-right-color: var(--fill-color);\n",
-              "    }\n",
-              "    80% {\n",
-              "      border-color: transparent;\n",
-              "      border-right-color: var(--fill-color);\n",
-              "      border-bottom-color: var(--fill-color);\n",
-              "    }\n",
-              "    90% {\n",
-              "      border-color: transparent;\n",
-              "      border-bottom-color: var(--fill-color);\n",
-              "    }\n",
-              "  }\n",
-              "</style>\n",
-              "\n",
-              "  <script>\n",
-              "    async function quickchart(key) {\n",
-              "      const quickchartButtonEl =\n",
-              "        document.querySelector('#' + key + ' button');\n",
-              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
-              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
-              "      try {\n",
-              "        const charts = await google.colab.kernel.invokeFunction(\n",
-              "            'suggestCharts', [key], {});\n",
-              "      } catch (error) {\n",
-              "        console.error('Error during call to suggestCharts:', error);\n",
-              "      }\n",
-              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
-              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
-              "    }\n",
-              "    (() => {\n",
-              "      let quickchartButtonEl =\n",
-              "        document.querySelector('#df-857b100f-363e-41f4-8e2a-0628457e85bc button');\n",
-              "      quickchartButtonEl.style.display =\n",
-              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
-              "    })();\n",
-              "  </script>\n",
-              "</div>\n",
-              "    </div>\n",
-              "  </div>\n"
-            ],
-            "application/vnd.google.colaboratory.intrinsic+json": {
-              "type": "dataframe",
-              "summary": "{\n  \"name\": \"fg\",\n  \"rows\": 5,\n  \"fields\": [\n    {\n      \"column\": \"id\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 1,\n        \"min\": 0,\n        \"max\": 4,\n        \"samples\": [\n          1,\n          4,\n          2\n        ],\n        \"num_unique_values\": 5,\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
-            }
-          },
-          "metadata": {},
-          "execution_count": 8
-        }
-      ],
-      "source": [
-        "fg = graphistry.edges(df, 's', 'd').materialize_nodes()\n",
-        "print(fg._nodes.shape, fg._edges.shape)\n",
-        "fg._nodes.head(5)"
-      ]
-    },
-    {
-      "cell_type": "markdown",
-      "source": [
-        "with 2 and 5 hop `chain` comparison we see a slight/negligable speedup enabled by setting g. to `cudf`"
-      ],
-      "metadata": {
-        "id": "2gVDho9cn2Et"
-      }
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "for n_hop in [2,5]:\n",
-        "    start0 = time.time()\n",
-        "    for i in range(100):\n",
-        "        fg2 = fg.chain([n({'id': 0}), e_forward(hops=n_hop)])  # using n notation\n",
-        "    mid0 = time.time()\n",
-        "    for i in range(100):\n",
-        "        fg2 = fg.chain([e_forward(source_node_match={'id': 0}, hops=n_hop)])  # using source_node_match in e_forward\n",
-        "    end0 = time.time()\n",
-        "    T0 = mid0-start0\n",
-        "    T1 = end0-mid0\n",
-        "    fg_gdf = fg.nodes(lambda g: cudf.DataFrame(g._nodes)).edges(lambda g: cudf.DataFrame(g._edges))\n",
-        "    start1 = time.time()\n",
-        "    for i in range(100):\n",
-        "        fg2 = fg_gdf.chain([n({'id': 0}), e_forward(hops=n_hop)])\n",
-        "    mid1 = time.time()\n",
-        "    for i in range(100):\n",
-        "        fg2 = fg_gdf.chain([e_forward(source_node_match={'id': 0}, hops=n_hop)])\n",
-        "    end1 = time.time()\n",
-        "    # print(fg._nodes.shape, fg._edges.shape)\n",
-        "    # print(fg2._nodes.shape, fg2._edges.shape)\n",
-        "    del fg_gdf\n",
-        "    del fg2\n",
-        "    T2 = mid1-start1\n",
-        "    T3 = end1-mid1\n",
-        "    print('\\nhops:',n_hop,'\\nCPU n_notation time:',np.round(T0,4),'\\nGPU n_notation time:',np.round(T2,4),'\\nspeedup:', np.round(T0/T2,4),\n",
-        "          '\\nCPU source_node_match time:',np.round(T1,4),'\\nGPU source_node_match time:',np.round(T3,4),'\\nspeedup:', np.round(T1/T3,4), )"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "ZKzoqGcdxekr",
-        "outputId": "344b9823-6998-4f71-d3b5-7aff9fec7912"
-      },
-      "execution_count": null,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "hops: 2 \n",
-            "CPU n_notation time: 13.6357 \n",
-            "GPU n_notation time: 12.2177 \n",
-            "n_notation speedup: 1.1161 \n",
-            "CPU source_node_match time: 21.2028 \n",
-            "GPU source_node_match time: 14.3844 \n",
-            "source_node_match speedup: 1.474\n",
-            "hops: 5 \n",
-            "CPU n_notation time: 36.8941 \n",
-            "GPU n_notation time: 21.3562 \n",
-            "n_notation speedup: 1.7276 \n",
-            "CPU source_node_match time: 17.8739 \n",
-            "GPU source_node_match time: 14.8514 \n",
-            "source_node_match speedup: 1.2035\n"
-          ]
-        }
-      ]
-    },
-    {
-      "cell_type": "markdown",
-      "source": [
-        "and with simple 2 and 5 hop `hop` comparison we see a 2x speedup enabled by setting g. to `cudf`"
-      ],
-      "metadata": {
-        "id": "5-7M9sPEAf5Z"
-      }
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "for n_hop in [2,5]:\n",
-        "    start_nodes = pd.DataFrame({fg._node: [0]})\n",
-        "    start0 = time.time()\n",
-        "    for i in range(100):\n",
-        "        fg2 = fg.hop(\n",
-        "            nodes=start_nodes,\n",
-        "            direction='forward',\n",
-        "            hops=n_hop)\n",
-        "    end0 = time.time()\n",
-        "    T0 = end0-start0\n",
-        "    start_nodes = cudf.DataFrame({fg._node: [0]})\n",
-        "    fg_gdf = fg.nodes(cudf.from_pandas(fg._nodes)).edges(cudf.from_pandas(fg._edges))\n",
-        "    start1 = time.time()\n",
-        "    for i in range(100):\n",
-        "        fg2 = fg_gdf.hop(\n",
-        "            nodes=start_nodes,\n",
-        "            direction='forward',\n",
-        "            hops=n_hop)\n",
-        "    end1 = time.time()\n",
-        "    # print(fg._nodes.shape, fg._edges.shape)\n",
-        "    # print(fg2._nodes.shape, fg2._edges.shape)\n",
-        "    del fg_gdf\n",
-        "    del fg2\n",
-        "    T1 = end1-start1\n",
-        "    print('\\nCPU',n_hop,'hop time:',np.round(T0,4),'\\nGPU',n_hop,'hop time:',np.round(T1,4),'\\nspeedup:', np.round(T0/T1,4))"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "Tki_0-_j3XKG",
-        "outputId": "7edbb4e9-1f49-4b7a-fdb4-9df0867512cd"
-      },
-      "execution_count": null,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "\n",
-            "CPU 2 hop time: 5.7415 \n",
-            "GPU 2 hop time: 2.7301 2 \n",
-            "hop speedup: 2.103\n",
-            "\n",
-            "CPU 5 hop time: 14.3391 \n",
-            "GPU 5 hop time: 6.9998 5 \n",
-            "hop speedup: 2.0485\n"
-          ]
-        }
-      ]
-    },
-    {
-      "cell_type": "markdown",
-      "metadata": {
-        "id": "KrJKjXy2KLos"
-      },
-      "source": [
-        "<a name=\"tw\"></a>\n",
-        "## Twitter\n",
-        "\n",
-        "- edges: 2420766\n",
-        "- nodes: 81306"
-      ]
-    },
-    {
-      "cell_type": "code",
-      "execution_count": null,
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "fO2qasGqpubr",
-        "outputId": "957c5ea8-0da9-4101-ecf8-7db8d5d13f49"
-      },
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "--2024-02-20 09:48:59--  https://snap.stanford.edu/data/twitter_combined.txt.gz\n",
-            "Resolving snap.stanford.edu (snap.stanford.edu)... 171.64.75.80\n",
-            "Connecting to snap.stanford.edu (snap.stanford.edu)|171.64.75.80|:443... connected.\n",
-            "HTTP request sent, awaiting response... 200 OK\n",
-            "Length: 10621918 (10M) [application/x-gzip]\n",
-            "Saving to: ‘twitter_combined.txt.gz’\n",
-            "\n",
-            "twitter_combined.tx 100%[===================>]  10.13M  9.10MB/s    in 1.1s    \n",
-            "\n",
-            "2024-02-20 09:49:00 (9.10 MB/s) - ‘twitter_combined.txt.gz’ saved [10621918/10621918]\n",
-            "\n"
-          ]
-        }
-      ],
-      "source": [
-        "! wget 'https://snap.stanford.edu/data/twitter_combined.txt.gz'\n",
-        "#! curl -L 'https://snap.stanford.edu/data/twitter_combined.txt.gz' -o twitter_combined.txt.gz"
-      ]
-    },
-    {
-      "cell_type": "code",
-      "execution_count": null,
-      "metadata": {
-        "id": "fn7zeA3SGlEo"
-      },
-      "outputs": [],
-      "source": [
-        "! gunzip twitter_combined.txt.gz"
-      ]
-    },
-    {
-      "cell_type": "code",
-      "execution_count": null,
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "68TAZkhLGz9g",
-        "outputId": "b861bc74-a142-4880-dc43-8068f7ef6b04"
-      },
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "214328887 34428380\n",
-            "17116707 28465635\n",
-            "380580781 18996905\n",
-            "221036078 153460275\n",
-            "107830991 17868918\n"
-          ]
-        }
-      ],
-      "source": [
-        "! head -n 5 twitter_combined.txt"
-      ]
-    },
-    {
-      "cell_type": "code",
-      "execution_count": null,
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "QU2wNeGXG2GC",
-        "outputId": "dff04552-efc7-49a6-9f25-460f31a288be"
-      },
-      "outputs": [
-        {
-          "output_type": "execute_result",
-          "data": {
-            "text/plain": [
-              "(2420766, 2)"
-            ]
-          },
-          "metadata": {},
-          "execution_count": 31
-        }
-      ],
-      "source": [
-        "te_df = pd.read_csv('twitter_combined.txt', sep=' ', names=['s', 'd'])\n",
-        "te_df.shape"
-      ]
-    },
-    {
-      "cell_type": "code",
-      "execution_count": null,
-      "metadata": {
-        "id": "EK5gQH2iG5UU"
-      },
-      "outputs": [],
-      "source": [
-        "import graphistry"
-      ]
-    },
-    {
-      "cell_type": "code",
-      "execution_count": null,
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "ZtIW-eFGG_R4",
-        "outputId": "53bd4e96-f3c4-4d45-abfd-e8a454a8ac7e"
-      },
-      "outputs": [
-        {
-          "output_type": "execute_result",
-          "data": {
-            "text/plain": [
-              "(81306, 1)"
-            ]
-          },
-          "metadata": {},
-          "execution_count": 33
-        }
-      ],
-      "source": [
-        "g = graphistry.edges(te_df, 's', 'd').materialize_nodes()\n",
-        "g._nodes.shape"
-      ]
-    },
-    {
-      "cell_type": "markdown",
-      "source": [
-        "on the twitter data, simpler `chain` operations over several different hops -- **10-20x** *italicized text* speed increases"
-      ],
-      "metadata": {
-        "id": "yR9Qr8tGww3b"
-      }
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "for n_hop in [1,2,8]:\n",
-        "    start_nodes = pd.DataFrame({fg._node: [0]})\n",
-        "    start0 = time.time()\n",
-        "    for i in range(10):\n",
-        "        g2 = g.chain([n({'id': 17116707}), e_forward(hops=n_hop)])\n",
-        "    end0 = time.time()\n",
-        "    T0 = end0-start0\n",
-        "    g_gdf = g.nodes(lambda g: cudf.DataFrame(g._nodes)).edges(lambda g: cudf.DataFrame(g._edges))\n",
-        "    start1 = time.time()\n",
-        "    for i in range(10):\n",
-        "        out = g_gdf.chain([n({'id': 17116707}), e_forward(hops=n_hop)])._nodes\n",
-        "    end1 = time.time()\n",
-        "    # print(fg._nodes.shape, fg._edges.shape)\n",
-        "    # print(fg2._nodes.shape, fg2._edges.shape)\n",
-        "    del g_gdf\n",
-        "    del out\n",
-        "    T1 = end1-start1\n",
-        "    print('\\nCPU',n_hop,'hop chain time:',np.round(T0,4),'\\nGPU',n_hop,'hop chain time:',np.round(T1,4),'\\nspeedup:', np.round(T0/T1,4))"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "rCsvQJa-6U0x",
-        "outputId": "70887aac-1bc8-499a-dc9e-40a1803e8fe3"
-      },
-      "execution_count": null,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "\n",
-            "CPU 1 hop chain time: 20.1676 \n",
-            "GPU 1 hop chain time: 1.0259 \n",
-            " 1 hop chain speedup: 19.6579\n",
-            "\n",
-            "CPU 2 hop chain time: 21.7168 \n",
-            "GPU 2 hop chain time: 2.2507 \n",
-            " 2 hop chain speedup: 9.6488\n",
-            "\n",
-            "CPU 8 hop chain time: 157.5035 \n",
-            "GPU 8 hop chain time: 7.8694 \n",
-            " 8 hop chain speedup: 20.0147\n"
-          ]
-        }
-      ]
-    },
-    {
-      "cell_type": "markdown",
-      "source": [
-        "and similarly for these `hop` operations -- **10-40x** speed increases"
-      ],
-      "metadata": {
-        "id": "gHHhyYlzArjw"
-      }
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "for n_hop in [1,2,8]:\n",
-        "    start_nodes = pd.DataFrame({g._node: [17116707]})\n",
-        "    start0 = time.time()\n",
-        "    for i in range(10):\n",
-        "      g2 = g.hop(\n",
-        "          nodes=start_nodes,\n",
-        "          direction='forward',\n",
-        "          hops=n_hop)\n",
-        "    end0 = time.time()\n",
-        "    T0 = end0-start0\n",
-        "    start_nodes = cudf.DataFrame({g._node: [17116707]})\n",
-        "    g_gdf = g.nodes(cudf.from_pandas(g._nodes)).edges(cudf.from_pandas(g._edges))\n",
-        "    start1 = time.time()\n",
-        "    for i in range(10):\n",
-        "        g2 = g_gdf.hop(\n",
-        "            nodes=start_nodes,\n",
-        "            direction='forward',\n",
-        "            hops=5)\n",
-        "    end1 = time.time()\n",
-        "    # print(fg._nodes.shape, fg._edges.shape)\n",
-        "    # print(fg2._nodes.shape, fg2._edges.shape)\n",
-        "    del start_nodes\n",
-        "    del g_gdf\n",
-        "    del g2\n",
-        "    T1 = end1-start1\n",
-        "    print('\\nCPU',n_hop,'hop chain time:',np.round(T0,4),'\\nGPU',n_hop,'hop chain time:',np.round(T1,4),'\\nspeedup:', np.round(T0/T1,4))"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "cnILbPnG7tf4",
-        "outputId": "bd4aa370-3b54-4c18-c92d-7aba957f658a"
-      },
-      "execution_count": null,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "\n",
-            "CPU 1 hop chain time: 12.3446 \n",
-            "GPU 1 hop chain time: 1.204 \n",
-            "speedup: 10.2526\n",
-            "\n",
-            "CPU 2 hop chain time: 13.2377 \n",
-            "GPU 2 hop chain time: 1.1608 \n",
-            "speedup: 11.4037\n",
-            "\n",
-            "CPU 8 hop chain time: 52.2491 \n",
-            "GPU 8 hop chain time: 1.2148 \n",
-            "speedup: 43.012\n"
-          ]
-        }
-      ]
-    },
-    {
-      "cell_type": "markdown",
-      "metadata": {
-        "id": "9dZzAAVONCD2"
-      },
-      "source": [
-        "<a name=\"gpl\"></a>\n",
-        "## GPlus\n",
-        "\n",
-        "- edges: 30494866\n",
-        "- nodes: 107614"
-      ]
-    },
-    {
-      "cell_type": "code",
-      "execution_count": null,
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "-nhWGNekKpcZ",
-        "outputId": "0ce5e0c8-e5a4-4e8e-b595-3c544192bf24"
-      },
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "--2024-02-20 09:59:24--  https://snap.stanford.edu/data/gplus_combined.txt.gz\n",
-            "Resolving snap.stanford.edu (snap.stanford.edu)... 171.64.75.80\n",
-            "Connecting to snap.stanford.edu (snap.stanford.edu)|171.64.75.80|:443... connected.\n",
-            "HTTP request sent, awaiting response... 200 OK\n",
-            "Length: 398930514 (380M) [application/x-gzip]\n",
-            "Saving to: ‘gplus_combined.txt.gz’\n",
-            "\n",
-            "gplus_combined.txt. 100%[===================>] 380.45M  39.7MB/s    in 9.9s    \n",
-            "\n",
-            "2024-02-20 09:59:34 (38.5 MB/s) - ‘gplus_combined.txt.gz’ saved [398930514/398930514]\n",
-            "\n"
-          ]
-        }
-      ],
-      "source": [
-        "! wget https://snap.stanford.edu/data/gplus_combined.txt.gz"
-      ]
-    },
-    {
-      "cell_type": "code",
-      "execution_count": null,
-      "metadata": {
-        "id": "g5wgA_c2KqwJ"
-      },
-      "outputs": [],
-      "source": [
-        "! gunzip gplus_combined.txt.gz"
-      ]
-    },
-    {
-      "cell_type": "code",
-      "execution_count": null,
-      "metadata": {
-        "id": "52hgDbr0Kti6",
-        "colab": {
-          "base_uri": "https://localhost:8080/",
-          "height": 260
-        },
-        "outputId": "1b81b614-f1b9-4031-db25-42ed9500c9c7"
-      },
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "(30494866, 2)\n",
-            "CPU times: user 16.8 s, sys: 1.41 s, total: 18.2 s\n",
-            "Wall time: 18.4 s\n"
-          ]
-        },
-        {
-          "output_type": "execute_result",
-          "data": {
-            "text/plain": [
-              "                       s                      d\n",
-              "0  116374117927631468606  101765416973555767821\n",
-              "1  112188647432305746617  107727150903234299458\n",
-              "2  116719211656774388392  100432456209427807893\n",
-              "3  117421021456205115327  101096322838605097368\n",
-              "4  116407635616074189669  113556266482860931616"
-            ],
-            "text/html": [
-              "\n",
-              "  <div id=\"df-37002e89-7515-49d9-996e-3ff42df86c6d\" class=\"colab-df-container\">\n",
-              "    <div>\n",
-              "<style scoped>\n",
-              "    .dataframe tbody tr th:only-of-type {\n",
-              "        vertical-align: middle;\n",
-              "    }\n",
-              "\n",
-              "    .dataframe tbody tr th {\n",
-              "        vertical-align: top;\n",
-              "    }\n",
-              "\n",
-              "    .dataframe thead th {\n",
-              "        text-align: right;\n",
-              "    }\n",
-              "</style>\n",
-              "<table border=\"1\" class=\"dataframe\">\n",
-              "  <thead>\n",
-              "    <tr style=\"text-align: right;\">\n",
-              "      <th></th>\n",
-              "      <th>s</th>\n",
-              "      <th>d</th>\n",
-              "    </tr>\n",
-              "  </thead>\n",
-              "  <tbody>\n",
-              "    <tr>\n",
-              "      <th>0</th>\n",
-              "      <td>116374117927631468606</td>\n",
-              "      <td>101765416973555767821</td>\n",
-              "    </tr>\n",
-              "    <tr>\n",
-              "      <th>1</th>\n",
-              "      <td>112188647432305746617</td>\n",
-              "      <td>107727150903234299458</td>\n",
-              "    </tr>\n",
-              "    <tr>\n",
-              "      <th>2</th>\n",
-              "      <td>116719211656774388392</td>\n",
-              "      <td>100432456209427807893</td>\n",
-              "    </tr>\n",
-              "    <tr>\n",
-              "      <th>3</th>\n",
-              "      <td>117421021456205115327</td>\n",
-              "      <td>101096322838605097368</td>\n",
-              "    </tr>\n",
-              "    <tr>\n",
-              "      <th>4</th>\n",
-              "      <td>116407635616074189669</td>\n",
-              "      <td>113556266482860931616</td>\n",
-              "    </tr>\n",
-              "  </tbody>\n",
-              "</table>\n",
-              "</div>\n",
-              "    <div class=\"colab-df-buttons\">\n",
-              "\n",
-              "  <div class=\"colab-df-container\">\n",
-              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-37002e89-7515-49d9-996e-3ff42df86c6d')\"\n",
-              "            title=\"Convert this dataframe to an interactive table.\"\n",
-              "            style=\"display:none;\">\n",
-              "\n",
-              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
-              "    <path d=\"M120-120v-720h720v720H120Zm60-500h600v-160H180v160Zm220 220h160v-160H400v160Zm0 220h160v-160H400v160ZM180-400h160v-160H180v160Zm440 0h160v-160H620v160ZM180-180h160v-160H180v160Zm440 0h160v-160H620v160Z\"/>\n",
-              "  </svg>\n",
-              "    </button>\n",
-              "\n",
-              "  <style>\n",
-              "    .colab-df-container {\n",
-              "      display:flex;\n",
-              "      gap: 12px;\n",
-              "    }\n",
-              "\n",
-              "    .colab-df-convert {\n",
-              "      background-color: #E8F0FE;\n",
-              "      border: none;\n",
-              "      border-radius: 50%;\n",
-              "      cursor: pointer;\n",
-              "      display: none;\n",
-              "      fill: #1967D2;\n",
-              "      height: 32px;\n",
-              "      padding: 0 0 0 0;\n",
-              "      width: 32px;\n",
-              "    }\n",
-              "\n",
-              "    .colab-df-convert:hover {\n",
-              "      background-color: #E2EBFA;\n",
-              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
-              "      fill: #174EA6;\n",
-              "    }\n",
-              "\n",
-              "    .colab-df-buttons div {\n",
-              "      margin-bottom: 4px;\n",
-              "    }\n",
-              "\n",
-              "    [theme=dark] .colab-df-convert {\n",
-              "      background-color: #3B4455;\n",
-              "      fill: #D2E3FC;\n",
-              "    }\n",
-              "\n",
-              "    [theme=dark] .colab-df-convert:hover {\n",
-              "      background-color: #434B5C;\n",
-              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
-              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
-              "      fill: #FFFFFF;\n",
-              "    }\n",
-              "  </style>\n",
-              "\n",
-              "    <script>\n",
-              "      const buttonEl =\n",
-              "        document.querySelector('#df-37002e89-7515-49d9-996e-3ff42df86c6d button.colab-df-convert');\n",
-              "      buttonEl.style.display =\n",
-              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
-              "\n",
-              "      async function convertToInteractive(key) {\n",
-              "        const element = document.querySelector('#df-37002e89-7515-49d9-996e-3ff42df86c6d');\n",
-              "        const dataTable =\n",
-              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
-              "                                                    [key], {});\n",
-              "        if (!dataTable) return;\n",
-              "\n",
-              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
-              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
-              "          + ' to learn more about interactive tables.';\n",
-              "        element.innerHTML = '';\n",
-              "        dataTable['output_type'] = 'display_data';\n",
-              "        await google.colab.output.renderOutput(dataTable, element);\n",
-              "        const docLink = document.createElement('div');\n",
-              "        docLink.innerHTML = docLinkHtml;\n",
-              "        element.appendChild(docLink);\n",
-              "      }\n",
-              "    </script>\n",
-              "  </div>\n",
-              "\n",
-              "\n",
-              "<div id=\"df-326e44f5-428e-4864-8700-ac2ce6e933f4\">\n",
-              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-326e44f5-428e-4864-8700-ac2ce6e933f4')\"\n",
-              "            title=\"Suggest charts\"\n",
-              "            style=\"display:none;\">\n",
-              "\n",
-              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
-              "     width=\"24px\">\n",
-              "    <g>\n",
-              "        <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
-              "    </g>\n",
-              "</svg>\n",
-              "  </button>\n",
-              "\n",
-              "<style>\n",
-              "  .colab-df-quickchart {\n",
-              "      --bg-color: #E8F0FE;\n",
-              "      --fill-color: #1967D2;\n",
-              "      --hover-bg-color: #E2EBFA;\n",
-              "      --hover-fill-color: #174EA6;\n",
-              "      --disabled-fill-color: #AAA;\n",
-              "      --disabled-bg-color: #DDD;\n",
-              "  }\n",
-              "\n",
-              "  [theme=dark] .colab-df-quickchart {\n",
-              "      --bg-color: #3B4455;\n",
-              "      --fill-color: #D2E3FC;\n",
-              "      --hover-bg-color: #434B5C;\n",
-              "      --hover-fill-color: #FFFFFF;\n",
-              "      --disabled-bg-color: #3B4455;\n",
-              "      --disabled-fill-color: #666;\n",
-              "  }\n",
-              "\n",
-              "  .colab-df-quickchart {\n",
-              "    background-color: var(--bg-color);\n",
-              "    border: none;\n",
-              "    border-radius: 50%;\n",
-              "    cursor: pointer;\n",
-              "    display: none;\n",
-              "    fill: var(--fill-color);\n",
-              "    height: 32px;\n",
-              "    padding: 0;\n",
-              "    width: 32px;\n",
-              "  }\n",
-              "\n",
-              "  .colab-df-quickchart:hover {\n",
-              "    background-color: var(--hover-bg-color);\n",
-              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
-              "    fill: var(--button-hover-fill-color);\n",
-              "  }\n",
-              "\n",
-              "  .colab-df-quickchart-complete:disabled,\n",
-              "  .colab-df-quickchart-complete:disabled:hover {\n",
-              "    background-color: var(--disabled-bg-color);\n",
-              "    fill: var(--disabled-fill-color);\n",
-              "    box-shadow: none;\n",
-              "  }\n",
-              "\n",
-              "  .colab-df-spinner {\n",
-              "    border: 2px solid var(--fill-color);\n",
-              "    border-color: transparent;\n",
-              "    border-bottom-color: var(--fill-color);\n",
-              "    animation:\n",
-              "      spin 1s steps(1) infinite;\n",
-              "  }\n",
-              "\n",
-              "  @keyframes spin {\n",
-              "    0% {\n",
-              "      border-color: transparent;\n",
-              "      border-bottom-color: var(--fill-color);\n",
-              "      border-left-color: var(--fill-color);\n",
-              "    }\n",
-              "    20% {\n",
-              "      border-color: transparent;\n",
-              "      border-left-color: var(--fill-color);\n",
-              "      border-top-color: var(--fill-color);\n",
-              "    }\n",
-              "    30% {\n",
-              "      border-color: transparent;\n",
-              "      border-left-color: var(--fill-color);\n",
-              "      border-top-color: var(--fill-color);\n",
-              "      border-right-color: var(--fill-color);\n",
-              "    }\n",
-              "    40% {\n",
-              "      border-color: transparent;\n",
-              "      border-right-color: var(--fill-color);\n",
-              "      border-top-color: var(--fill-color);\n",
-              "    }\n",
-              "    60% {\n",
-              "      border-color: transparent;\n",
-              "      border-right-color: var(--fill-color);\n",
-              "    }\n",
-              "    80% {\n",
-              "      border-color: transparent;\n",
-              "      border-right-color: var(--fill-color);\n",
-              "      border-bottom-color: var(--fill-color);\n",
-              "    }\n",
-              "    90% {\n",
-              "      border-color: transparent;\n",
-              "      border-bottom-color: var(--fill-color);\n",
-              "    }\n",
-              "  }\n",
-              "</style>\n",
-              "\n",
-              "  <script>\n",
-              "    async function quickchart(key) {\n",
-              "      const quickchartButtonEl =\n",
-              "        document.querySelector('#' + key + ' button');\n",
-              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
-              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
-              "      try {\n",
-              "        const charts = await google.colab.kernel.invokeFunction(\n",
-              "            'suggestCharts', [key], {});\n",
-              "      } catch (error) {\n",
-              "        console.error('Error during call to suggestCharts:', error);\n",
-              "      }\n",
-              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
-              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
-              "    }\n",
-              "    (() => {\n",
-              "      let quickchartButtonEl =\n",
-              "        document.querySelector('#df-326e44f5-428e-4864-8700-ac2ce6e933f4 button');\n",
-              "      quickchartButtonEl.style.display =\n",
-              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
-              "    })();\n",
-              "  </script>\n",
-              "</div>\n",
-              "    </div>\n",
-              "  </div>\n"
-            ],
-            "application/vnd.google.colaboratory.intrinsic+json": {
-              "type": "dataframe",
-              "summary": "{\n  \"name\": \"get_ipython()\",\n  \"rows\": 5,\n  \"fields\": [\n    {\n      \"column\": \"s\",\n      \"properties\": {\n        \"dtype\": \"string\",\n        \"samples\": [\n          \"112188647432305746617\",\n          \"116407635616074189669\",\n          \"116719211656774388392\"\n        ],\n        \"num_unique_values\": 5,\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"d\",\n      \"properties\": {\n        \"dtype\": \"string\",\n        \"samples\": [\n          \"107727150903234299458\",\n          \"113556266482860931616\",\n          \"100432456209427807893\"\n        ],\n        \"num_unique_values\": 5,\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
-            }
-          },
-          "metadata": {},
-          "execution_count": 41
-        }
-      ],
-      "source": [
-        "%%time\n",
-        "ge_df = pd.read_csv('gplus_combined.txt', sep=' ', names=['s', 'd'])\n",
-        "print(ge_df.shape)\n",
-        "ge_df.head(5)"
-      ]
-    },
-    {
-      "cell_type": "code",
-      "execution_count": null,
-      "metadata": {
-        "id": "w5YkN-nLK6UV",
-        "colab": {
-          "base_uri": "https://localhost:8080/",
-          "height": 260
-        },
-        "outputId": "9c818e80-34b1-431a-d965-3305b45c1bb2"
-      },
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "(30494866, 2) (107614, 1)\n",
-            "CPU times: user 4.41 s, sys: 1.29 s, total: 5.7 s\n",
-            "Wall time: 5.69 s\n"
-          ]
-        },
-        {
-          "output_type": "execute_result",
-          "data": {
-            "text/plain": [
-              "                      id\n",
-              "0  116374117927631468606\n",
-              "1  112188647432305746617\n",
-              "2  116719211656774388392\n",
-              "3  117421021456205115327\n",
-              "4  116407635616074189669"
-            ],
-            "text/html": [
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-              "    <div>\n",
-              "<style scoped>\n",
-              "    .dataframe tbody tr th:only-of-type {\n",
-              "        vertical-align: middle;\n",
-              "    }\n",
-              "\n",
-              "    .dataframe tbody tr th {\n",
-              "        vertical-align: top;\n",
-              "    }\n",
-              "\n",
-              "    .dataframe thead th {\n",
-              "        text-align: right;\n",
-              "    }\n",
-              "</style>\n",
-              "<table border=\"1\" class=\"dataframe\">\n",
-              "  <thead>\n",
-              "    <tr style=\"text-align: right;\">\n",
-              "      <th></th>\n",
-              "      <th>id</th>\n",
-              "    </tr>\n",
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-              "      <td>117421021456205115327</td>\n",
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-              "      <th>4</th>\n",
-              "      <td>116407635616074189669</td>\n",
-              "    </tr>\n",
-              "  </tbody>\n",
-              "</table>\n",
-              "</div>\n",
-              "    <div class=\"colab-df-buttons\">\n",
-              "\n",
-              "  <div class=\"colab-df-container\">\n",
-              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-18b91552-c868-4cde-8c8f-cef30e769b69')\"\n",
-              "            title=\"Convert this dataframe to an interactive table.\"\n",
-              "            style=\"display:none;\">\n",
-              "\n",
-              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
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-              "  </svg>\n",
-              "    </button>\n",
-              "\n",
-              "  <style>\n",
-              "    .colab-df-container {\n",
-              "      display:flex;\n",
-              "      gap: 12px;\n",
-              "    }\n",
-              "\n",
-              "    .colab-df-convert {\n",
-              "      background-color: #E8F0FE;\n",
-              "      border: none;\n",
-              "      border-radius: 50%;\n",
-              "      cursor: pointer;\n",
-              "      display: none;\n",
-              "      fill: #1967D2;\n",
-              "      height: 32px;\n",
-              "      padding: 0 0 0 0;\n",
-              "      width: 32px;\n",
-              "    }\n",
-              "\n",
-              "    .colab-df-convert:hover {\n",
-              "      background-color: #E2EBFA;\n",
-              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
-              "      fill: #174EA6;\n",
-              "    }\n",
-              "\n",
-              "    .colab-df-buttons div {\n",
-              "      margin-bottom: 4px;\n",
-              "    }\n",
-              "\n",
-              "    [theme=dark] .colab-df-convert {\n",
-              "      background-color: #3B4455;\n",
-              "      fill: #D2E3FC;\n",
-              "    }\n",
-              "\n",
-              "    [theme=dark] .colab-df-convert:hover {\n",
-              "      background-color: #434B5C;\n",
-              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
-              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
-              "      fill: #FFFFFF;\n",
-              "    }\n",
-              "  </style>\n",
-              "\n",
-              "    <script>\n",
-              "      const buttonEl =\n",
-              "        document.querySelector('#df-18b91552-c868-4cde-8c8f-cef30e769b69 button.colab-df-convert');\n",
-              "      buttonEl.style.display =\n",
-              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
-              "\n",
-              "      async function convertToInteractive(key) {\n",
-              "        const element = document.querySelector('#df-18b91552-c868-4cde-8c8f-cef30e769b69');\n",
-              "        const dataTable =\n",
-              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
-              "                                                    [key], {});\n",
-              "        if (!dataTable) return;\n",
-              "\n",
-              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
-              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
-              "          + ' to learn more about interactive tables.';\n",
-              "        element.innerHTML = '';\n",
-              "        dataTable['output_type'] = 'display_data';\n",
-              "        await google.colab.output.renderOutput(dataTable, element);\n",
-              "        const docLink = document.createElement('div');\n",
-              "        docLink.innerHTML = docLinkHtml;\n",
-              "        element.appendChild(docLink);\n",
-              "      }\n",
-              "    </script>\n",
-              "  </div>\n",
-              "\n",
-              "\n",
-              "<div id=\"df-164b8618-a7e8-4900-b561-e308fc38c946\">\n",
-              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-164b8618-a7e8-4900-b561-e308fc38c946')\"\n",
-              "            title=\"Suggest charts\"\n",
-              "            style=\"display:none;\">\n",
-              "\n",
-              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
-              "     width=\"24px\">\n",
-              "    <g>\n",
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-              "    </g>\n",
-              "</svg>\n",
-              "  </button>\n",
-              "\n",
-              "<style>\n",
-              "  .colab-df-quickchart {\n",
-              "      --bg-color: #E8F0FE;\n",
-              "      --fill-color: #1967D2;\n",
-              "      --hover-bg-color: #E2EBFA;\n",
-              "      --hover-fill-color: #174EA6;\n",
-              "      --disabled-fill-color: #AAA;\n",
-              "      --disabled-bg-color: #DDD;\n",
-              "  }\n",
-              "\n",
-              "  [theme=dark] .colab-df-quickchart {\n",
-              "      --bg-color: #3B4455;\n",
-              "      --fill-color: #D2E3FC;\n",
-              "      --hover-bg-color: #434B5C;\n",
-              "      --hover-fill-color: #FFFFFF;\n",
-              "      --disabled-bg-color: #3B4455;\n",
-              "      --disabled-fill-color: #666;\n",
-              "  }\n",
-              "\n",
-              "  .colab-df-quickchart {\n",
-              "    background-color: var(--bg-color);\n",
-              "    border: none;\n",
-              "    border-radius: 50%;\n",
-              "    cursor: pointer;\n",
-              "    display: none;\n",
-              "    fill: var(--fill-color);\n",
-              "    height: 32px;\n",
-              "    padding: 0;\n",
-              "    width: 32px;\n",
-              "  }\n",
-              "\n",
-              "  .colab-df-quickchart:hover {\n",
-              "    background-color: var(--hover-bg-color);\n",
-              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
-              "    fill: var(--button-hover-fill-color);\n",
-              "  }\n",
-              "\n",
-              "  .colab-df-quickchart-complete:disabled,\n",
-              "  .colab-df-quickchart-complete:disabled:hover {\n",
-              "    background-color: var(--disabled-bg-color);\n",
-              "    fill: var(--disabled-fill-color);\n",
-              "    box-shadow: none;\n",
-              "  }\n",
-              "\n",
-              "  .colab-df-spinner {\n",
-              "    border: 2px solid var(--fill-color);\n",
-              "    border-color: transparent;\n",
-              "    border-bottom-color: var(--fill-color);\n",
-              "    animation:\n",
-              "      spin 1s steps(1) infinite;\n",
-              "  }\n",
-              "\n",
-              "  @keyframes spin {\n",
-              "    0% {\n",
-              "      border-color: transparent;\n",
-              "      border-bottom-color: var(--fill-color);\n",
-              "      border-left-color: var(--fill-color);\n",
-              "    }\n",
-              "    20% {\n",
-              "      border-color: transparent;\n",
-              "      border-left-color: var(--fill-color);\n",
-              "      border-top-color: var(--fill-color);\n",
-              "    }\n",
-              "    30% {\n",
-              "      border-color: transparent;\n",
-              "      border-left-color: var(--fill-color);\n",
-              "      border-top-color: var(--fill-color);\n",
-              "      border-right-color: var(--fill-color);\n",
-              "    }\n",
-              "    40% {\n",
-              "      border-color: transparent;\n",
-              "      border-right-color: var(--fill-color);\n",
-              "      border-top-color: var(--fill-color);\n",
-              "    }\n",
-              "    60% {\n",
-              "      border-color: transparent;\n",
-              "      border-right-color: var(--fill-color);\n",
-              "    }\n",
-              "    80% {\n",
-              "      border-color: transparent;\n",
-              "      border-right-color: var(--fill-color);\n",
-              "      border-bottom-color: var(--fill-color);\n",
-              "    }\n",
-              "    90% {\n",
-              "      border-color: transparent;\n",
-              "      border-bottom-color: var(--fill-color);\n",
-              "    }\n",
-              "  }\n",
-              "</style>\n",
-              "\n",
-              "  <script>\n",
-              "    async function quickchart(key) {\n",
-              "      const quickchartButtonEl =\n",
-              "        document.querySelector('#' + key + ' button');\n",
-              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
-              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
-              "      try {\n",
-              "        const charts = await google.colab.kernel.invokeFunction(\n",
-              "            'suggestCharts', [key], {});\n",
-              "      } catch (error) {\n",
-              "        console.error('Error during call to suggestCharts:', error);\n",
-              "      }\n",
-              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
-              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
-              "    }\n",
-              "    (() => {\n",
-              "      let quickchartButtonEl =\n",
-              "        document.querySelector('#df-164b8618-a7e8-4900-b561-e308fc38c946 button');\n",
-              "      quickchartButtonEl.style.display =\n",
-              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
-              "    })();\n",
-              "  </script>\n",
-              "</div>\n",
-              "    </div>\n",
-              "  </div>\n"
-            ],
-            "application/vnd.google.colaboratory.intrinsic+json": {
-              "type": "dataframe",
-              "summary": "{\n  \"name\": \"get_ipython()\",\n  \"rows\": 5,\n  \"fields\": [\n    {\n      \"column\": \"id\",\n      \"properties\": {\n        \"dtype\": \"string\",\n        \"samples\": [\n          \"112188647432305746617\",\n          \"116407635616074189669\",\n          \"116719211656774388392\"\n        ],\n        \"num_unique_values\": 5,\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
-            }
-          },
-          "metadata": {},
-          "execution_count": 42
-        }
-      ],
-      "source": [
-        "%%time\n",
-        "gg = graphistry.edges(ge_df, 's', 'd').materialize_nodes()\n",
-        "gg = graphistry.edges(ge_df, 's', 'd').nodes(gg._nodes, 'id')\n",
-        "print(gg._edges.shape, gg._nodes.shape)\n",
-        "gg._nodes.head(5)"
-      ]
-    },
-    {
-      "cell_type": "code",
-      "execution_count": null,
-      "metadata": {
-        "id": "NKtz54uELX-8",
-        "colab": {
-          "base_uri": "https://localhost:8080/",
-          "height": 116
-        },
-        "outputId": "aaccd673-85c1-40a4-ccdc-f13388e7a01a"
-      },
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "CPU times: user 471 ms, sys: 307 ms, total: 779 ms\n",
-            "Wall time: 776 ms\n"
-          ]
-        },
-        {
-          "output_type": "execute_result",
-          "data": {
-            "text/plain": [
-              "                      id\n",
-              "0  116374117927631468606"
-            ],
-            "text/html": [
-              "\n",
-              "  <div id=\"df-9891edfd-d16e-4aae-953d-3763664284ff\" class=\"colab-df-container\">\n",
-              "    <div>\n",
-              "<style scoped>\n",
-              "    .dataframe tbody tr th:only-of-type {\n",
-              "        vertical-align: middle;\n",
-              "    }\n",
-              "\n",
-              "    .dataframe tbody tr th {\n",
-              "        vertical-align: top;\n",
-              "    }\n",
-              "\n",
-              "    .dataframe thead th {\n",
-              "        text-align: right;\n",
-              "    }\n",
-              "</style>\n",
-              "<table border=\"1\" class=\"dataframe\">\n",
-              "  <thead>\n",
-              "    <tr style=\"text-align: right;\">\n",
-              "      <th></th>\n",
-              "      <th>id</th>\n",
-              "    </tr>\n",
-              "  </thead>\n",
-              "  <tbody>\n",
-              "    <tr>\n",
-              "      <th>0</th>\n",
-              "      <td>116374117927631468606</td>\n",
-              "    </tr>\n",
-              "  </tbody>\n",
-              "</table>\n",
-              "</div>\n",
-              "    <div class=\"colab-df-buttons\">\n",
-              "\n",
-              "  <div class=\"colab-df-container\">\n",
-              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-9891edfd-d16e-4aae-953d-3763664284ff')\"\n",
-              "            title=\"Convert this dataframe to an interactive table.\"\n",
-              "            style=\"display:none;\">\n",
-              "\n",
-              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
-              "    <path d=\"M120-120v-720h720v720H120Zm60-500h600v-160H180v160Zm220 220h160v-160H400v160Zm0 220h160v-160H400v160ZM180-400h160v-160H180v160Zm440 0h160v-160H620v160ZM180-180h160v-160H180v160Zm440 0h160v-160H620v160Z\"/>\n",
-              "  </svg>\n",
-              "    </button>\n",
-              "\n",
-              "  <style>\n",
-              "    .colab-df-container {\n",
-              "      display:flex;\n",
-              "      gap: 12px;\n",
-              "    }\n",
-              "\n",
-              "    .colab-df-convert {\n",
-              "      background-color: #E8F0FE;\n",
-              "      border: none;\n",
-              "      border-radius: 50%;\n",
-              "      cursor: pointer;\n",
-              "      display: none;\n",
-              "      fill: #1967D2;\n",
-              "      height: 32px;\n",
-              "      padding: 0 0 0 0;\n",
-              "      width: 32px;\n",
-              "    }\n",
-              "\n",
-              "    .colab-df-convert:hover {\n",
-              "      background-color: #E2EBFA;\n",
-              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
-              "      fill: #174EA6;\n",
-              "    }\n",
-              "\n",
-              "    .colab-df-buttons div {\n",
-              "      margin-bottom: 4px;\n",
-              "    }\n",
-              "\n",
-              "    [theme=dark] .colab-df-convert {\n",
-              "      background-color: #3B4455;\n",
-              "      fill: #D2E3FC;\n",
-              "    }\n",
-              "\n",
-              "    [theme=dark] .colab-df-convert:hover {\n",
-              "      background-color: #434B5C;\n",
-              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
-              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
-              "      fill: #FFFFFF;\n",
-              "    }\n",
-              "  </style>\n",
-              "\n",
-              "    <script>\n",
-              "      const buttonEl =\n",
-              "        document.querySelector('#df-9891edfd-d16e-4aae-953d-3763664284ff button.colab-df-convert');\n",
-              "      buttonEl.style.display =\n",
-              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
-              "\n",
-              "      async function convertToInteractive(key) {\n",
-              "        const element = document.querySelector('#df-9891edfd-d16e-4aae-953d-3763664284ff');\n",
-              "        const dataTable =\n",
-              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
-              "                                                    [key], {});\n",
-              "        if (!dataTable) return;\n",
-              "\n",
-              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
-              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
-              "          + ' to learn more about interactive tables.';\n",
-              "        element.innerHTML = '';\n",
-              "        dataTable['output_type'] = 'display_data';\n",
-              "        await google.colab.output.renderOutput(dataTable, element);\n",
-              "        const docLink = document.createElement('div');\n",
-              "        docLink.innerHTML = docLinkHtml;\n",
-              "        element.appendChild(docLink);\n",
-              "      }\n",
-              "    </script>\n",
-              "  </div>\n",
-              "\n",
-              "    </div>\n",
-              "  </div>\n"
-            ],
-            "application/vnd.google.colaboratory.intrinsic+json": {
-              "type": "dataframe",
-              "summary": "{\n  \"name\": \"get_ipython()\",\n  \"rows\": 1,\n  \"fields\": [\n    {\n      \"column\": \"id\",\n      \"properties\": {\n        \"dtype\": \"string\",\n        \"samples\": [\n          \"116374117927631468606\"\n        ],\n        \"num_unique_values\": 1,\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
-            }
-          },
-          "metadata": {},
-          "execution_count": 43
-        }
-      ],
-      "source": [
-        "%%time\n",
-        "gg.chain([ n({'id': '116374117927631468606'})])._nodes"
-      ]
-    },
-    {
-      "cell_type": "markdown",
-      "source": [
-        "on the GPlus data, simpler `chain` operations over several different hops -- **100-200x** speed increases"
-      ],
-      "metadata": {
-        "id": "e4ZchWvrBKdY"
-      }
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "for n_hop in [1,2,3,4,5]:\n",
-        "    start_nodes = pd.DataFrame({fg._node: [0]})\n",
-        "    start0 = time.time()\n",
-        "    out = gg.chain([ n({'id': '116374117927631468606'}), e_forward(hops=n_hop)])._nodes\n",
-        "    end0 = time.time()\n",
-        "    T0 = end0-start0\n",
-        "    gg_gdf = gg.nodes(lambda g: cudf.DataFrame(g._nodes)).edges(lambda g: cudf.DataFrame(g._edges))\n",
-        "    start1 = time.time()\n",
-        "    out = gg_gdf.chain([ n({'id': '116374117927631468606'}), e_forward(hops=n_hop)])\n",
-        "    end1 = time.time()\n",
-        "    # print(fg._nodes.shape, fg._edges.shape)\n",
-        "    # print(fg2._nodes.shape, fg2._edges.shape)\n",
-        "    del gg_gdf\n",
-        "    del out\n",
-        "    T1 = end1-start1\n",
-        "    print('\\nCPU',n_hop,'hop chain time:',np.round(T0,4),'\\nGPU',n_hop,'hop chain time:',np.round(T1,4),'\\nspeedup:', np.round(T0/T1,4))"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/",
-          "height": 507
-        },
-        "id": "fTnU8MLr8tV5",
-        "outputId": "40a2f455-9d79-4a3c-abeb-aac93713a424"
-      },
-      "execution_count": null,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "\n",
-            "CPU 1 hop chain time: 70.7013 \n",
-            "GPU 1 hop chain time: 0.2911 \n",
-            "speedup: 242.9049\n",
-            "\n",
-            "CPU 2 hop chain time: 84.2395 \n",
-            "GPU 2 hop chain time: 0.6138 \n",
-            "speedup: 137.252\n"
-          ]
-        },
-        {
-          "output_type": "error",
-          "ename": "KeyboardInterrupt",
-          "evalue": "",
-          "traceback": [
-            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-            "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
-            "\u001b[0;32m<ipython-input-46-c29c7daea5b2>\u001b[0m in \u001b[0;36m<cell line: 1>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      2\u001b[0m     \u001b[0mstart_nodes\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpd\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mDataFrame\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m{\u001b[0m\u001b[0mfg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_node\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m     \u001b[0mstart0\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtime\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtime\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m     \u001b[0mout\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mgg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mchain\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m \u001b[0mn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m{\u001b[0m\u001b[0;34m'id'\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;34m'116374117927631468606'\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0me_forward\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mhops\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mn_hop\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_nodes\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      5\u001b[0m     \u001b[0mend0\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtime\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtime\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m     \u001b[0mT0\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mend0\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mstart0\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/graphistry/compute/ComputeMixin.py\u001b[0m in \u001b[0;36mchain\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n\u001b[1;32m    391\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    392\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mchain\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 393\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mchain_base\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    394\u001b[0m     \u001b[0mchain\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__doc__\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mchain_base\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__doc__\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/graphistry/compute/chain.py\u001b[0m in \u001b[0;36mchain\u001b[0;34m(self, ops, engine)\u001b[0m\n\u001b[1;32m    285\u001b[0m         )\n\u001b[1;32m    286\u001b[0m         g_step = (\n\u001b[0;32m--> 287\u001b[0;31m             op(\n\u001b[0m\u001b[1;32m    288\u001b[0m                 \u001b[0mg\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mg\u001b[0m\u001b[0;34m,\u001b[0m  \u001b[0;31m# transition via any original edge\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    289\u001b[0m                 \u001b[0mprev_node_wavefront\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mprev_step_nodes\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/graphistry/compute/ast.py\u001b[0m in \u001b[0;36m__call__\u001b[0;34m(self, g, prev_node_wavefront, target_wave_front, engine)\u001b[0m\n\u001b[1;32m    326\u001b[0m             \u001b[0mlogger\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdebug\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'----------------------------------------'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    327\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 328\u001b[0;31m         out_g = g.hop(\n\u001b[0m\u001b[1;32m    329\u001b[0m             \u001b[0mnodes\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mprev_node_wavefront\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    330\u001b[0m             \u001b[0mhops\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mhops\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/graphistry/compute/ComputeMixin.py\u001b[0m in \u001b[0;36mhop\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n\u001b[1;32m    379\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    380\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mhop\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 381\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mhop_base\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    382\u001b[0m     \u001b[0mhop\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__doc__\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mhop_base\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__doc__\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    383\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
-            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/graphistry/compute/hop.py\u001b[0m in \u001b[0;36mhop\u001b[0;34m(self, nodes, hops, to_fixed_point, direction, edge_match, source_node_match, destination_node_match, source_node_query, destination_node_query, edge_query, return_as_wave_front, target_wave_front, engine)\u001b[0m\n\u001b[1;32m    188\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mdirection\u001b[0m \u001b[0;32min\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m'forward'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'undirected'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    189\u001b[0m             hop_edges_forward = (\n\u001b[0;32m--> 190\u001b[0;31m                 wave_front_iter.merge(\n\u001b[0m\u001b[1;32m    191\u001b[0m                     \u001b[0medges_indexed\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mg2\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_source\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mg2\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_destination\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mEDGE_ID\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0massign\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;34m{\u001b[0m\u001b[0mg2\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_node\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0medges_indexed\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mg2\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_source\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    192\u001b[0m                     \u001b[0mhow\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'inner'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/pandas/core/frame.py\u001b[0m in \u001b[0;36mmerge\u001b[0;34m(self, right, how, on, left_on, right_on, left_index, right_index, sort, suffixes, copy, indicator, validate)\u001b[0m\n\u001b[1;32m  10091\u001b[0m         \u001b[0;32mfrom\u001b[0m \u001b[0mpandas\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcore\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreshape\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmerge\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mmerge\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m  10092\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m> 10093\u001b[0;31m         return merge(\n\u001b[0m\u001b[1;32m  10094\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m  10095\u001b[0m             \u001b[0mright\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/pandas/core/reshape/merge.py\u001b[0m in \u001b[0;36mmerge\u001b[0;34m(left, right, how, on, left_on, right_on, left_index, right_index, sort, suffixes, copy, indicator, validate)\u001b[0m\n\u001b[1;32m    122\u001b[0m         \u001b[0mvalidate\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mvalidate\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    123\u001b[0m     )\n\u001b[0;32m--> 124\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mop\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_result\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcopy\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mcopy\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    125\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    126\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
-            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/pandas/core/reshape/merge.py\u001b[0m in \u001b[0;36mget_result\u001b[0;34m(self, copy)\u001b[0m\n\u001b[1;32m    771\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mleft\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mright\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_indicator_pre_merge\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mleft\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mright\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    772\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 773\u001b[0;31m         \u001b[0mjoin_index\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mleft_indexer\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mright_indexer\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_get_join_info\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    774\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    775\u001b[0m         result = self._reindex_and_concat(\n",
-            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/pandas/core/reshape/merge.py\u001b[0m in \u001b[0;36m_get_join_info\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m   1024\u001b[0m             )\n\u001b[1;32m   1025\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1026\u001b[0;31m             \u001b[0;34m(\u001b[0m\u001b[0mleft_indexer\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mright_indexer\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_get_join_indexers\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1027\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1028\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mright_index\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/pandas/core/reshape/merge.py\u001b[0m in \u001b[0;36m_get_join_indexers\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    998\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m_get_join_indexers\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m->\u001b[0m \u001b[0mtuple\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mnpt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mNDArray\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mintp\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnpt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mNDArray\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mintp\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    999\u001b[0m         \u001b[0;34m\"\"\"return the join indexers\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1000\u001b[0;31m         return get_join_indexers(\n\u001b[0m\u001b[1;32m   1001\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mleft_join_keys\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mright_join_keys\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msort\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msort\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhow\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mhow\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1002\u001b[0m         )\n",
-            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/pandas/core/reshape/merge.py\u001b[0m in \u001b[0;36mget_join_indexers\u001b[0;34m(left_keys, right_keys, sort, how, **kwargs)\u001b[0m\n\u001b[1;32m   1583\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mn\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mleft_keys\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1584\u001b[0m     )\n\u001b[0;32m-> 1585\u001b[0;31m     \u001b[0mzipped\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mzip\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mmapped\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1586\u001b[0m     \u001b[0mllab\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrlab\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mshape\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mlist\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mx\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mzipped\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1587\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
-            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/pandas/core/reshape/merge.py\u001b[0m in \u001b[0;36m<genexpr>\u001b[0;34m(.0)\u001b[0m\n\u001b[1;32m   1580\u001b[0m     \u001b[0;31m# get left & right join labels and num. of levels at each location\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1581\u001b[0m     mapped = (\n\u001b[0;32m-> 1582\u001b[0;31m         \u001b[0m_factorize_keys\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mleft_keys\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mright_keys\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msort\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0msort\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhow\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mhow\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1583\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mn\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mleft_keys\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1584\u001b[0m     )\n",
-            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/pandas/core/reshape/merge.py\u001b[0m in \u001b[0;36m_factorize_keys\u001b[0;34m(lk, rk, sort, how)\u001b[0m\n\u001b[1;32m   2331\u001b[0m     \u001b[0;31m# \"Union[ndarray[Any, dtype[signedinteger[_64Bit]]],\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2332\u001b[0m     \u001b[0;31m# ndarray[Any, dtype[object_]]]\"; expected \"ndarray[Any, dtype[object_]]\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2333\u001b[0;31m     \u001b[0mrlab\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mrizer\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfactorize\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrk\u001b[0m\u001b[0;34m)\u001b[0m  \u001b[0;31m# type: ignore[arg-type]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   2334\u001b[0m     \u001b[0;32massert\u001b[0m \u001b[0mllab\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdtype\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdtype\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mintp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mllab\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdtype\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2335\u001b[0m     \u001b[0;32massert\u001b[0m \u001b[0mrlab\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdtype\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdtype\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mintp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrlab\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdtype\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-            "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
-          ]
-        }
-      ]
-    },
-    {
-      "cell_type": "markdown",
-      "source": [
-        "and similarly for these hop operations -- **100x** speed increases"
-      ],
-      "metadata": {
-        "id": "80bs6Y5pBWb2"
-      }
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "for n_hop in [1,2,3,4,5]:\n",
-        "    start_nodes = pd.DataFrame({gg._node: ['116374117927631468606']})\n",
-        "    start0 = time.time()\n",
-        "    for i in range(1):\n",
-        "      g2 = gg.hop(\n",
-        "          nodes=start_nodes,\n",
-        "          direction='forward',\n",
-        "          hops=n_hop)\n",
-        "    end0 = time.time()\n",
-        "    T0 = end0-start0\n",
-        "    start_nodes = cudf.DataFrame({gg._node: ['116374117927631468606']})\n",
-        "    gg_gdf = gg.nodes(cudf.from_pandas(gg._nodes)).edges(cudf.from_pandas(gg._edges))\n",
-        "    start1 = time.time()\n",
-        "    for i in range(1):\n",
-        "      g2 = gg_gdf.hop(\n",
-        "          nodes=start_nodes,\n",
-        "          direction='forward',\n",
-        "          hops=n_hop)\n",
-        "    end1 = time.time()\n",
-        "    # print(fg._nodes.shape, fg._edges.shape)\n",
-        "    # print(fg2._nodes.shape, fg2._edges.shape)\n",
-        "    del start_nodes\n",
-        "    del gg_gdf\n",
-        "    del g2\n",
-        "    T1 = end1-start1\n",
-        "    print('\\nCPU',n_hop,'hop chain time:',np.round(T0,4),'\\nGPU',n_hop,'hop chain time:',np.round(T1,4),'\\nspeedup:', np.round(T0/T1,4))"
-      ],
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "N2-gDFod9vc3",
-        "outputId": "c6967f1f-fa01-41a6-a776-02e2892f300f"
-      },
-      "execution_count": null,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "\n",
-            "CPU 1 hop chain time: 38.0714 \n",
-            "GPU 1 hop chain time: 0.2615 \n",
-            "speedup: 145.5678\n",
-            "\n",
-            "CPU 2 hop chain time: 52.949 \n",
-            "GPU 2 hop chain time: 0.4553 \n",
-            "speedup: 116.2876\n"
-          ]
-        }
-      ]
-    },
-    {
-      "cell_type": "markdown",
-      "metadata": {
-        "id": "R03M_swxarKC"
-      },
-      "source": [
-        "<a name=\"ork\"></a>\n",
-        "## Orkut\n",
-        "- 117M edges\n",
-        "- 3M nodes"
-      ]
-    },
-    {
-      "cell_type": "code",
-      "execution_count": null,
-      "metadata": {
-        "id": "QoabYR2maxPo",
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "outputId": "f58e2837-9417-490b-882c-b1f478ed53f8"
-      },
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "--2024-02-19 06:02:00--  https://snap.stanford.edu/data/bigdata/communities/com-orkut.ungraph.txt.gz\n",
-            "Resolving snap.stanford.edu (snap.stanford.edu)... 171.64.75.80\n",
-            "Connecting to snap.stanford.edu (snap.stanford.edu)|171.64.75.80|:443... connected.\n",
-            "HTTP request sent, awaiting response... 200 OK\n",
-            "Length: 447251958 (427M) [application/x-gzip]\n",
-            "Saving to: ‘com-orkut.ungraph.txt.gz’\n",
-            "\n",
-            "com-orkut.ungraph.t 100%[===================>] 426.53M  31.8MB/s    in 11s     \n",
-            "\n",
-            "2024-02-19 06:02:11 (37.4 MB/s) - ‘com-orkut.ungraph.txt.gz’ saved [447251958/447251958]\n",
-            "\n"
-          ]
-        }
-      ],
-      "source": [
-        "! wget https://snap.stanford.edu/data/bigdata/communities/com-orkut.ungraph.txt.gz"
-      ]
-    },
-    {
-      "cell_type": "code",
-      "execution_count": null,
-      "metadata": {
-        "id": "BvvfFPKWbAVJ"
-      },
-      "outputs": [],
-      "source": [
-        "! gunzip com-orkut.ungraph.txt.gz"
-      ]
-    },
-    {
-      "cell_type": "code",
-      "execution_count": null,
-      "metadata": {
-        "id": "YsWwRoPqbPIb",
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "outputId": "5c12501a-e724-44d5-f651-e1860a8638af"
-      },
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "# Undirected graph: ../../data/output/orkut.txt\n",
-            "# Orkut\n",
-            "# Nodes: 3072441 Edges: 117185083\n",
-            "# FromNodeId\tToNodeId\n",
-            "1\t2\n",
-            "1\t3\n",
-            "1\t4\n"
-          ]
-        }
-      ],
-      "source": [
-        "! head -n 7 com-orkut.ungraph.txt"
-      ]
-    },
-    {
-      "cell_type": "code",
-      "execution_count": null,
-      "metadata": {
-        "id": "cbMC8r2ldjbW",
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "outputId": "87ee2818-72d9-46e7-d0d8-5d16958e10c8"
-      },
-      "outputs": [
-        {
-          "output_type": "execute_result",
-          "data": {
-            "text/plain": [
-              "('24.02.01', '0.33.0')"
-            ]
-          },
-          "metadata": {},
-          "execution_count": 8
-        }
-      ],
-      "source": [
-        "import pandas as pd\n",
-        "\n",
-        "import graphistry\n",
-        "\n",
-        "from graphistry import (\n",
-        "\n",
-        "    # graph operators\n",
-        "    n, e_undirected, e_forward, e_reverse,\n",
-        "\n",
-        "    # attribute predicates\n",
-        "    is_in, ge, startswith, contains, match as match_re\n",
-        ")\n",
-        "\n",
-        "import cudf\n",
-        "\n",
-        "#work around google colab shell encoding bugs\n",
-        "import locale\n",
-        "locale.getpreferredencoding = lambda: \"UTF-8\"\n",
-        "\n",
-        "cudf.__version__, graphistry.__version__"
-      ]
-    },
-    {
-      "cell_type": "code",
-      "execution_count": null,
-      "metadata": {
-        "id": "TopFxAvnh_Cv",
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "outputId": "52288638-691e-47e4-87fc-4f761a3e9302"
-      },
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "Mon Feb 19 06:02:29 2024       \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| NVIDIA-SMI 535.104.05             Driver Version: 535.104.05   CUDA Version: 12.2     |\n",
-            "|-----------------------------------------+----------------------+----------------------+\n",
-            "| GPU  Name                 Persistence-M | Bus-Id        Disp.A | Volatile Uncorr. ECC |\n",
-            "| Fan  Temp   Perf          Pwr:Usage/Cap |         Memory-Usage | GPU-Util  Compute M. |\n",
-            "|                                         |                      |               MIG M. |\n",
-            "|=========================================+======================+======================|\n",
-            "|   0  Tesla T4                       Off | 00000000:00:04.0 Off |                    0 |\n",
-            "| N/A   64C    P0              29W /  70W |    111MiB / 15360MiB |      0%      Default |\n",
-            "|                                         |                      |                  N/A |\n",
-            "+-----------------------------------------+----------------------+----------------------+\n",
-            "                                                                                         \n",
-            "+---------------------------------------------------------------------------------------+\n",
-            "| Processes:                                                                            |\n",
-            "|  GPU   GI   CI        PID   Type   Process name                            GPU Memory |\n",
-            "|        ID   ID                                                             Usage      |\n",
-            "|=======================================================================================|\n",
-            "+---------------------------------------------------------------------------------------+\n"
-          ]
-        }
-      ],
-      "source": [
-        "! nvidia-smi"
-      ]
-    },
-    {
-      "cell_type": "code",
-      "execution_count": null,
-      "metadata": {
-        "id": "Oczs87ITbJgw",
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "outputId": "b894db9b-13d1-426a-b162-dea780abce3b"
-      },
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "(117185082, 2)\n",
-            "   s  d\n",
-            "0  1  3\n",
-            "1  1  4\n",
-            "2  1  5\n",
-            "3  1  6\n",
-            "4  1  7\n",
-            "s    int64\n",
-            "d    int64\n",
-            "dtype: object\n",
-            "CPU times: user 2.34 s, sys: 1.29 s, total: 3.63 s\n",
-            "Wall time: 3.77 s\n"
-          ]
-        }
-      ],
-      "source": [
-        "%%time\n",
-        "co_df = cudf.read_csv('com-orkut.ungraph.txt', sep='\\t', names=['s', 'd'], skiprows=5).to_pandas()\n",
-        "print(co_df.shape)\n",
-        "print(co_df.head(5))\n",
-        "print(co_df.dtypes)\n",
-        "#del co_df"
-      ]
-    },
-    {
-      "cell_type": "markdown",
-      "source": [
-        "from load into gpu and back to cpu again"
-      ],
-      "metadata": {
-        "id": "2QLDI3vdAtkf"
-      }
-    },
-    {
-      "cell_type": "code",
-      "execution_count": null,
-      "metadata": {
-        "id": "gGSDjTtveFAT",
-        "colab": {
-          "base_uri": "https://localhost:8080/",
-          "height": 260
-        },
-        "outputId": "d8501df9-7070-4bfa-c5e2-49a581df5f56"
-      },
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "(3072441, 1) (117185082, 2)\n",
-            "CPU times: user 2.06 s, sys: 7.93 s, total: 10 s\n",
-            "Wall time: 11.2 s\n"
-          ]
-        },
-        {
-          "output_type": "execute_result",
-          "data": {
-            "text/plain": [
-              "   id\n",
-              "0   1\n",
-              "1   2\n",
-              "2   3\n",
-              "3   4\n",
-              "4   5"
-            ],
-            "text/html": [
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-              "    .colab-df-container {\n",
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-              "      gap: 12px;\n",
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-              "\n",
-              "    .colab-df-convert {\n",
-              "      background-color: #E8F0FE;\n",
-              "      border: none;\n",
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-              "      fill: #174EA6;\n",
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-              "\n",
-              "    .colab-df-buttons div {\n",
-              "      margin-bottom: 4px;\n",
-              "    }\n",
-              "\n",
-              "    [theme=dark] .colab-df-convert {\n",
-              "      background-color: #3B4455;\n",
-              "      fill: #D2E3FC;\n",
-              "    }\n",
-              "\n",
-              "    [theme=dark] .colab-df-convert:hover {\n",
-              "      background-color: #434B5C;\n",
-              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
-              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
-              "      fill: #FFFFFF;\n",
-              "    }\n",
-              "  </style>\n",
-              "\n",
-              "    <script>\n",
-              "      const buttonEl =\n",
-              "        document.querySelector('#df-1a654a77-93b5-4de8-97a3-bf1bbd1acda7 button.colab-df-convert');\n",
-              "      buttonEl.style.display =\n",
-              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
-              "\n",
-              "      async function convertToInteractive(key) {\n",
-              "        const element = document.querySelector('#df-1a654a77-93b5-4de8-97a3-bf1bbd1acda7');\n",
-              "        const dataTable =\n",
-              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
-              "                                                    [key], {});\n",
-              "        if (!dataTable) return;\n",
-              "\n",
-              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
-              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
-              "          + ' to learn more about interactive tables.';\n",
-              "        element.innerHTML = '';\n",
-              "        dataTable['output_type'] = 'display_data';\n",
-              "        await google.colab.output.renderOutput(dataTable, element);\n",
-              "        const docLink = document.createElement('div');\n",
-              "        docLink.innerHTML = docLinkHtml;\n",
-              "        element.appendChild(docLink);\n",
-              "      }\n",
-              "    </script>\n",
-              "  </div>\n",
-              "\n",
-              "\n",
-              "<div id=\"df-81e3ded9-c90b-4696-9661-cffe40b3414c\">\n",
-              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-81e3ded9-c90b-4696-9661-cffe40b3414c')\"\n",
-              "            title=\"Suggest charts\"\n",
-              "            style=\"display:none;\">\n",
-              "\n",
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-              "    </g>\n",
-              "</svg>\n",
-              "  </button>\n",
-              "\n",
-              "<style>\n",
-              "  .colab-df-quickchart {\n",
-              "      --bg-color: #E8F0FE;\n",
-              "      --fill-color: #1967D2;\n",
-              "      --hover-bg-color: #E2EBFA;\n",
-              "      --hover-fill-color: #174EA6;\n",
-              "      --disabled-fill-color: #AAA;\n",
-              "      --disabled-bg-color: #DDD;\n",
-              "  }\n",
-              "\n",
-              "  [theme=dark] .colab-df-quickchart {\n",
-              "      --bg-color: #3B4455;\n",
-              "      --fill-color: #D2E3FC;\n",
-              "      --hover-bg-color: #434B5C;\n",
-              "      --hover-fill-color: #FFFFFF;\n",
-              "      --disabled-bg-color: #3B4455;\n",
-              "      --disabled-fill-color: #666;\n",
-              "  }\n",
-              "\n",
-              "  .colab-df-quickchart {\n",
-              "    background-color: var(--bg-color);\n",
-              "    border: none;\n",
-              "    border-radius: 50%;\n",
-              "    cursor: pointer;\n",
-              "    display: none;\n",
-              "    fill: var(--fill-color);\n",
-              "    height: 32px;\n",
-              "    padding: 0;\n",
-              "    width: 32px;\n",
-              "  }\n",
-              "\n",
-              "  .colab-df-quickchart:hover {\n",
-              "    background-color: var(--hover-bg-color);\n",
-              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
-              "    fill: var(--button-hover-fill-color);\n",
-              "  }\n",
-              "\n",
-              "  .colab-df-quickchart-complete:disabled,\n",
-              "  .colab-df-quickchart-complete:disabled:hover {\n",
-              "    background-color: var(--disabled-bg-color);\n",
-              "    fill: var(--disabled-fill-color);\n",
-              "    box-shadow: none;\n",
-              "  }\n",
-              "\n",
-              "  .colab-df-spinner {\n",
-              "    border: 2px solid var(--fill-color);\n",
-              "    border-color: transparent;\n",
-              "    border-bottom-color: var(--fill-color);\n",
-              "    animation:\n",
-              "      spin 1s steps(1) infinite;\n",
-              "  }\n",
-              "\n",
-              "  @keyframes spin {\n",
-              "    0% {\n",
-              "      border-color: transparent;\n",
-              "      border-bottom-color: var(--fill-color);\n",
-              "      border-left-color: var(--fill-color);\n",
-              "    }\n",
-              "    20% {\n",
-              "      border-color: transparent;\n",
-              "      border-left-color: var(--fill-color);\n",
-              "      border-top-color: var(--fill-color);\n",
-              "    }\n",
-              "    30% {\n",
-              "      border-color: transparent;\n",
-              "      border-left-color: var(--fill-color);\n",
-              "      border-top-color: var(--fill-color);\n",
-              "      border-right-color: var(--fill-color);\n",
-              "    }\n",
-              "    40% {\n",
-              "      border-color: transparent;\n",
-              "      border-right-color: var(--fill-color);\n",
-              "      border-top-color: var(--fill-color);\n",
-              "    }\n",
-              "    60% {\n",
-              "      border-color: transparent;\n",
-              "      border-right-color: var(--fill-color);\n",
-              "    }\n",
-              "    80% {\n",
-              "      border-color: transparent;\n",
-              "      border-right-color: var(--fill-color);\n",
-              "      border-bottom-color: var(--fill-color);\n",
-              "    }\n",
-              "    90% {\n",
-              "      border-color: transparent;\n",
-              "      border-bottom-color: var(--fill-color);\n",
-              "    }\n",
-              "  }\n",
-              "</style>\n",
-              "\n",
-              "  <script>\n",
-              "    async function quickchart(key) {\n",
-              "      const quickchartButtonEl =\n",
-              "        document.querySelector('#' + key + ' button');\n",
-              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
-              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
-              "      try {\n",
-              "        const charts = await google.colab.kernel.invokeFunction(\n",
-              "            'suggestCharts', [key], {});\n",
-              "      } catch (error) {\n",
-              "        console.error('Error during call to suggestCharts:', error);\n",
-              "      }\n",
-              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
-              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
-              "    }\n",
-              "    (() => {\n",
-              "      let quickchartButtonEl =\n",
-              "        document.querySelector('#df-81e3ded9-c90b-4696-9661-cffe40b3414c button');\n",
-              "      quickchartButtonEl.style.display =\n",
-              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
-              "    })();\n",
-              "  </script>\n",
-              "</div>\n",
-              "    </div>\n",
-              "  </div>\n"
-            ],
-            "application/vnd.google.colaboratory.intrinsic+json": {
-              "type": "dataframe",
-              "summary": "{\n  \"name\": \"get_ipython()\",\n  \"rows\": 5,\n  \"fields\": [\n    {\n      \"column\": \"id\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 1,\n        \"min\": 1,\n        \"max\": 5,\n        \"samples\": [\n          2,\n          5,\n          3\n        ],\n        \"num_unique_values\": 5,\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
-            }
-          },
-          "metadata": {},
-          "execution_count": 11
-        }
-      ],
-      "source": [
-        "%%time\n",
-        "co_g = graphistry.edges(cudf.DataFrame(co_df), 's', 'd').materialize_nodes(engine='cudf')\n",
-        "co_g = co_g.nodes(lambda g: g._nodes.to_pandas()).edges(lambda g: g._edges.to_pandas())\n",
-        "print(co_g._nodes.shape, co_g._edges.shape)\n",
-        "co_g._nodes.head(5)"
-      ]
-    },
-    {
-      "cell_type": "markdown",
-      "source": [
-        "on the Orkut data, simpler chain operations over several different hops -- **10-50x** speed increases"
-      ],
-      "metadata": {
-        "id": "G4f19-djBd7J"
-      }
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "for n_hop in [1,2,3,4,5,6]:\n",
-        "    start_nodes = pd.DataFrame({fg._node: [0]})\n",
-        "    start0 = time.time()\n",
-        "    for i in range(10):\n",
-        "        out = co_g.chain([ n({'id': 1}), e_forward(hops=n_hop)])._nodes\n",
-        "    end0 = time.time()\n",
-        "    T0 = end0-start0\n",
-        "    co_gdf = co_g.nodes(lambda g: cudf.DataFrame(g._nodes)).edges(lambda g: cudf.DataFrame(g._edges))\n",
-        "    start1 = time.time()\n",
-        "    for i in range(10):\n",
-        "        out = co_gdf.chain([ n({'id': 1}), e_forward(hops=n_hop)])    end1 = time.time()\n",
-        "    # print(fg._nodes.shape, fg._edges.shape)\n",
-        "    # print(fg2._nodes.shape, fg2._edges.shape)\n",
-        "    del co_gdf\n",
-        "    del out\n",
-        "    T1 = end1-start1\n",
-        "    print('\\nCPU',n_hop,'hop chain time:',np.round(T0,4),'\\nGPU',n_hop,'hop chain time:',np.round(T1,4),'\\nspeedup:', np.round(T0/T1,4))"
-      ],
-      "metadata": {
-        "id": "yWabsh_k-tgy"
-      },
-      "execution_count": null,
-      "outputs": []
-    },
-    {
-      "cell_type": "markdown",
-      "source": [
-        "and similarly for these hop operations -- 10-40x speed increases"
-      ],
-      "metadata": {
-        "id": "v-gVx5trBeSl"
-      }
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "for n_hop in [1,2,3,4,5]:\n",
-        "    start_nodes = pd.DataFrame({'id': [1]})\n",
-        "    start0 = time.time()\n",
-        "    for i in range(1):\n",
-        "      g2 = co_g.hop(\n",
-        "          nodes=start_nodes,\n",
-        "          direction='forward',\n",
-        "          hops=n_hop)\n",
-        "    end0 = time.time()\n",
-        "    T0 = end0-start0\n",
-        "    start_nodes = cudf.DataFrame({'id': [1]})\n",
-        "    co_gdf = co_g.nodes(lambda g: cudf.DataFrame(g._nodes)).edges(lambda g: cudf.DataFrame(g._edges))\n",
-        "    start1 = time.time()\n",
-        "    for i in range(1):\n",
-        "      g2 = gg_gdf.hop(\n",
-        "          nodes=start_nodes,\n",
-        "          direction='forward',\n",
-        "          hops=n_hop)\n",
-        "    end1 = time.time()\n",
-        "    # print(fg._nodes.shape, fg._edges.shape)\n",
-        "    # print(fg2._nodes.shape, fg2._edges.shape)\n",
-        "    del start_nodes\n",
-        "    del co_gdf\n",
-        "    del g2\n",
-        "    T1 = end1-start1\n",
-        "    print('\\nCPU',n_hop,'hop chain time:',np.round(T0,4),'\\nGPU',n_hop,'hop chain time:',np.round(T1,4),'\\nspeedup:', np.round(T0/T1,4))"
-      ],
-      "metadata": {
-        "id": "kHZatWCB_qwd"
-      },
-      "execution_count": null,
-      "outputs": []
-    },
-    {
-      "cell_type": "code",
-      "execution_count": null,
-      "metadata": {
-        "id": "eiXFImxF-rzw"
-      },
-      "outputs": [],
-      "source": [
-        "!lscpu\n"
-      ]
-    },
-    {
-      "cell_type": "code",
-      "execution_count": null,
-      "metadata": {
-        "id": "wJohLi58-sN5",
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "outputId": "07a499d6-3109-486e-d387-002abd133d22"
-      },
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "               total        used        free      shared  buff/cache   available\n",
-            "Mem:            12Gi       5.8Gi       1.6Gi       1.0Gi       5.2Gi       5.5Gi\n",
-            "Swap:             0B          0B          0B\n"
-          ]
-        }
-      ],
-      "source": [
-        "!free -h\n"
-      ]
-    },
-    {
-      "cell_type": "code",
-      "execution_count": null,
-      "metadata": {
-        "id": "Ygc2nrkznlCu"
-      },
-      "outputs": [],
-      "source": []
-    }
-  ],
-  "metadata": {
-    "accelerator": "GPU",
-    "colab": {
-      "gpuType": "T4",
-      "provenance": [],
-      "toc_visible": true,
-      "include_colab_link": true
-    },
-    "kernelspec": {
-      "display_name": "Python 3",
-      "name": "python3"
-    },
-    "language_info": {
-      "name": "python"
-    }
-  },
-  "nbformat": 4,
-  "nbformat_minor": 0
-}
\ No newline at end of file
diff --git a/demos/gfql/simple_gfql_notebook.ipynb b/demos/gfql/simple_gfql_notebook.ipynb
deleted file mode 100644
index 5f27f7b619..0000000000
--- a/demos/gfql/simple_gfql_notebook.ipynb
+++ /dev/null
@@ -1,264 +0,0 @@
-{
-  "nbformat": 4,
-  "nbformat_minor": 0,
-  "metadata": {
-    "colab": {
-      "provenance": [],
-      "gpuType": "T4",
-      "include_colab_link": true
-    },
-    "kernelspec": {
-      "name": "python3",
-      "display_name": "Python 3"
-    },
-    "language_info": {
-      "name": "python"
-    },
-    "accelerator": "GPU"
-  },
-  "cells": [
-    {
-      "cell_type": "markdown",
-      "metadata": {
-        "id": "view-in-github",
-        "colab_type": "text"
-      },
-      "source": [
-        "<a href=\"https://colab.research.google.com/github/dcolinmorgan/grph/blob/main/simple_GFQL.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
-      ]
-    },
-    {
-      "cell_type": "markdown",
-      "source": [
-        "# simple GFQL demo on Twitter data\n",
-        "\n",
-        "* Twitter\tNetwork with 81,306 Nodes\tand 2,420,766 Edges\n",
-        "\n",
-        "* The single-threaded CPU mode benefits from GFQL's novel dataframe engine, and the GPU mode further adds single-GPU acceleration. Both the chain() and hop() methods are examined.\n",
-        "\n",
-        "* The benchmark does not examine bigger-than-memory and distributed scenarios. The provided results here are from running on a free Google Colab T4 runtime, with a 2.2GHz Intel CPU (12 GB CPU RAM) and T4 Nvidia GPU (16 GB GPU RAM)."
-      ],
-      "metadata": {
-        "id": "Sm80AgJOJ3-c"
-      }
-    },
-    {
-      "cell_type": "markdown",
-      "source": [
-        "## Install, Import, Load"
-      ],
-      "metadata": {
-        "id": "g7s-qBKqE9eC"
-      }
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "# !pip install --extra-index-url=https://pypi.nvidia.com cuml-cu12 cudf-cu12\n",
-        "import cudf\n",
-        "cudf.__version__\n",
-        "\n",
-        "!pip install -q igraph\n",
-        "!pip install -q graphistry\n",
-        "\n",
-        "import pandas as pd\n",
-        "import graphistry, time, cProfile\n",
-        "\n",
-        "from graphistry import (\n",
-        "\n",
-        "    # graph operators\n",
-        "    n, e_undirected, e_forward, e_reverse,\n",
-        "\n",
-        "    # attribute predicates\n",
-        "    is_in, ge, startswith, contains, match as match_re\n",
-        ")\n",
-        "graphistry.__version__"
-      ],
-      "metadata": {
-        "id": "JTdSJgquBnGd",
-        "colab": {
-          "base_uri": "https://localhost:8080/",
-          "height": 35
-        },
-        "outputId": "4d1da186-28ab-4236-a569-4dd8760c4715"
-      },
-      "execution_count": 5,
-      "outputs": [
-        {
-          "output_type": "execute_result",
-          "data": {
-            "text/plain": [
-              "'0.33.0'"
-            ],
-            "application/vnd.google.colaboratory.intrinsic+json": {
-              "type": "string"
-            }
-          },
-          "metadata": {},
-          "execution_count": 5
-        }
-      ]
-    },
-    {
-      "cell_type": "code",
-      "execution_count": 2,
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "yLJjLYAWbRXH",
-        "outputId": "e0177c6d-7d74-449a-c72b-28241516aaf0"
-      },
-      "outputs": [
-        {
-          "output_type": "execute_result",
-          "data": {
-            "text/plain": [
-              "(81306, 1)"
-            ]
-          },
-          "metadata": {},
-          "execution_count": 2
-        }
-      ],
-      "source": [
-        "te_df = pd.read_csv('https://snap.stanford.edu/data/twitter_combined.txt.gz', sep=' ', names=['s', 'd'])\n",
-        "g = graphistry.edges(te_df, 's', 'd').materialize_nodes()"
-      ]
-    },
-    {
-      "cell_type": "markdown",
-      "source": [
-        "## .chain() CPU v GPU"
-      ],
-      "metadata": {
-        "id": "c3vuo0yVFDCs"
-      }
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "start = time.time()\n",
-        "\n",
-        "for i in range(10):\n",
-        "  g2 = g.chain([n({'id': 17116707}), e_forward(hops=1)])\n",
-        "g2._nodes.shape, g2._edges.shape\n",
-        "\n",
-        "end1 = time.time()\n",
-        "T1 = end1 - start"
-      ],
-      "metadata": {
-        "id": "wEzyOOymCcsj"
-      },
-      "execution_count": null,
-      "outputs": []
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "start = time.time()\n",
-        "\n",
-        "g_gdf = g.nodes(lambda g: cudf.DataFrame(g._nodes)).edges(lambda g: cudf.DataFrame(g._edges))\n",
-        "for i in range(10):\n",
-        "  out = g_gdf.chain([n({'id': 17116707}), e_forward(hops=1)])._nodes\n",
-        "del g_gdf\n",
-        "del out\n",
-        "\n",
-        "end2 = time.time()\n",
-        "T2= end2 - start\n",
-        "print('CPU time:',T1, '\\nGPU time:', T2, '\\nspeedup:', T1/T2)"
-      ],
-      "metadata": {
-        "id": "yKoNh5UgClIr",
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "outputId": "5c9545e1-5a6c-45db-b0ab-a199939e8ebd"
-      },
-      "execution_count": 17,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "CPU time: 17.837570190429688 \n",
-            "GPU time: 2.0647764205932617 \n",
-            "speedup: 8.638983868919091\n"
-          ]
-        }
-      ]
-    },
-    {
-      "cell_type": "markdown",
-      "source": [
-        "## .hop() CPU v GPU\n",
-        "\n",
-        "*   simpler tasks can witness greater speedup\n",
-        "\n"
-      ],
-      "metadata": {
-        "id": "KrXZ7ajHFJ3z"
-      }
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "start = time.time()\n",
-        "start_nodes = pd.DataFrame({g._node: [17116707]})\n",
-        "for i in range(10):\n",
-        "  g2 = g.hop(\n",
-        "      nodes=start_nodes,\n",
-        "      direction='forward',\n",
-        "      hops=8)\n",
-        "\n",
-        "end1 = time.time()\n",
-        "T1 = end1 - start"
-      ],
-      "metadata": {
-        "id": "CJt_8YTPCtZM"
-      },
-      "execution_count": null,
-      "outputs": []
-    },
-    {
-      "cell_type": "code",
-      "source": [
-        "start = time.time()\n",
-        "start_nodes = cudf.DataFrame({g._node: [17116707]})\n",
-        "g_gdf = g.nodes(cudf.from_pandas(g._nodes)).edges(cudf.from_pandas(g._edges))\n",
-        "for i in range(10):\n",
-        "  g2 = g_gdf.hop(\n",
-        "      nodes=start_nodes,\n",
-        "      direction='forward',\n",
-        "      engine = 'cudf',  # one can also set `engine = cudf`\n",
-        "      hops=8)\n",
-        "del start_nodes\n",
-        "del g_gdf\n",
-        "del g2\n",
-        "\n",
-        "end2 = time.time()\n",
-        "T2= end2 - start\n",
-        "print('CPU time:',T1, '\\nGPU time:', T2, '\\nspeedup:', T1/T2)"
-      ],
-      "metadata": {
-        "id": "fOC7ODIeFTI6",
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "outputId": "ba349462-caee-4f42-8f45-fa7c883c54bc"
-      },
-      "execution_count": 26,
-      "outputs": [
-        {
-          "output_type": "stream",
-          "name": "stdout",
-          "text": [
-            "CPU time: 40.91506862640381 \n",
-            "GPU time: 2.8351004123687744 \n",
-            "speedup: 14.431611821543413\n"
-          ]
-        }
-      ]
-    }
-  ]
-}
\ No newline at end of file

From e371bdf693fb78bc635dd2d34957e9a858543fe5 Mon Sep 17 00:00:00 2001
From: Daniel <dcolinmorgan@gmail.com>
Date: Fri, 12 Jul 2024 08:34:24 +0200
Subject: [PATCH 3/5] remove stale links

---
 README.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/README.md b/README.md
index 3a8fbb2166..5db55aa816 100644
--- a/README.md
+++ b/README.md
@@ -147,7 +147,7 @@ It is easy to turn arbitrary data into insightful graphs. PyGraphistry comes wit
     g2.plot()
     ```
 
-* GFQL: Cypher-style graph pattern mining queries on dataframes with optional GPU acceleration ([ipynb demo](demos/more_examples/graphistry_features/hop_and_chain_graph_pattern_mining.ipynb), [chain and hop demo](demos/gfql/simple_gfql_notebook.ipynb), [benchmark](demos/gfql/gfql_cpv_gpu_enchmark.ipynb)
+* GFQL: Cypher-style graph pattern mining queries on dataframes with optional GPU acceleration ([ipynb demo](demos/more_examples/graphistry_features/hop_and_chain_graph_pattern_mining.ipynb),[benchmark](demos/gfql/gfql_hops_cpu_gpu.ipynb)
 
   Run Cypher-style graph queries natively on dataframes without going to a database or Java with GFQL:
 
@@ -1248,7 +1248,7 @@ assert 'pagerank' in g2._nodes.columns
 
 PyGraphistry supports GFQL, its PyData-native variant of the popular Cypher graph query language, meaning you can do graph pattern matching directly from Pandas dataframes without installing a database or Java
 
-See also [graph pattern matching tutorial](demos/more_examples/graphistry_features/hop_and_chain_graph_pattern_mining.ipynb), [starting with chain and hop](demos/gfql/simple_gfql_notebook.ipynb) and the CPU/GPU [benchmark](demos/gfql/gfql_cpv_gpu_enchmark.ipynb)
+See also [graph pattern matching tutorial](demos/more_examples/graphistry_features/hop_and_chain_graph_pattern_mining.ipynb), and the CPU/GPU [benchmark](demos/gfql/gfql_hops_cpu_gpu.ipynb)
 
 Traverse within a graph, or expand one graph against another
 

From 3407edc9f1df2617a81bf97a81180c2334c6a84c Mon Sep 17 00:00:00 2001
From: Daniel <dcolinmorgan@gmail.com>
Date: Mon, 15 Jul 2024 16:05:21 +0200
Subject: [PATCH 4/5] resolve readme url x2

---
 README.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/README.md b/README.md
index 5db55aa816..cf131684cb 100644
--- a/README.md
+++ b/README.md
@@ -147,7 +147,7 @@ It is easy to turn arbitrary data into insightful graphs. PyGraphistry comes wit
     g2.plot()
     ```
 
-* GFQL: Cypher-style graph pattern mining queries on dataframes with optional GPU acceleration ([ipynb demo](demos/more_examples/graphistry_features/hop_and_chain_graph_pattern_mining.ipynb),[benchmark](demos/gfql/gfql_hops_cpu_gpu.ipynb)
+* GFQL: Cypher-style graph pattern mining queries on dataframes with optional GPU acceleration ([ipynb demo](demos/more_examples/graphistry_features/hop_and_chain_graph_pattern_mining.ipynb),[benchmark](demos/gfql/benchmark_hops_cpu_gpu.ipynb)
 
   Run Cypher-style graph queries natively on dataframes without going to a database or Java with GFQL:
 
@@ -1248,7 +1248,7 @@ assert 'pagerank' in g2._nodes.columns
 
 PyGraphistry supports GFQL, its PyData-native variant of the popular Cypher graph query language, meaning you can do graph pattern matching directly from Pandas dataframes without installing a database or Java
 
-See also [graph pattern matching tutorial](demos/more_examples/graphistry_features/hop_and_chain_graph_pattern_mining.ipynb), and the CPU/GPU [benchmark](demos/gfql/gfql_hops_cpu_gpu.ipynb)
+See also [graph pattern matching tutorial](demos/more_examples/graphistry_features/hop_and_chain_graph_pattern_mining.ipynb), and the CPU/GPU [benchmark](demos/gfql/benchmark_hops_cpu_gpu.ipynb)
 
 Traverse within a graph, or expand one graph against another
 

From 4f53be7254c80d6fb79332f9df1000d022032427 Mon Sep 17 00:00:00 2001
From: Daniel <dcolinmorgan@gmail.com>
Date: Wed, 7 Aug 2024 12:04:09 +0200
Subject: [PATCH 5/5] backout md url changes

---
 README.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/README.md b/README.md
index a50e260f76..afc7b6c832 100644
--- a/README.md
+++ b/README.md
@@ -147,7 +147,7 @@ It is easy to turn arbitrary data into insightful graphs. PyGraphistry comes wit
     g2.plot()
     ```
 
-* GFQL: Cypher-style graph pattern mining queries on dataframes with optional GPU acceleration ([ipynb demo](https://github.com/graphistry/pygraphistry/blob/master/demos/more_examples/graphistry_features/hop_and_chain_graph_pattern_mining.ipynb), [benchmark](https://github.com/graphistry/pygraphistry/blob/master/demos/gfql/benchmark_hops_cpu_gpu.ipynb))
+* GFQL: Cypher-style graph pattern mining queries on dataframes with optional GPU acceleration ([ipynb demo](demos/more_examples/graphistry_features/hop_and_chain_graph_pattern_mining.ipynb), [benchmark](demos/gfql/benchmark_hops_cpu_gpu.ipynb))
 
   Run Cypher-style graph queries natively on dataframes without going to a database or Java with GFQL:
 
@@ -1250,7 +1250,7 @@ assert 'pagerank' in g2._nodes.columns
 
 PyGraphistry supports GFQL, its PyData-native variant of the popular Cypher graph query language, meaning you can do graph pattern matching directly from Pandas dataframes without installing a database or Java
 
-See also [graph pattern matching tutorial](https://github.com/graphistry/pygraphistry/tree/master/demos/more_examples/graphistry_features/hop_and_chain_graph_pattern_mining.ipynb) and the CPU/GPU [benchmark](https://github.com/graphistry/pygraphistry/tree/master/demos/gfql/benchmark_hops_cpu_gpu.ipynb)
+See also [graph pattern matching tutorial](demos/more_examples/graphistry_features/hop_and_chain_graph_pattern_mining.ipynb) and the CPU/GPU [benchmark](demos/gfql/benchmark_hops_cpu_gpu.ipynb)
 
 Traverse within a graph, or expand one graph against another