k_core_range.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/shima-aflatounian/K-core-Networks/blob/main/k_core_range.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#Poe, *chatGPT* Code\n",
        "import networkx as nx\n",
        "import matplotlib.pyplot as plt\n",
        "import random\n",
        "\n",
        "# Generate a random network graph\n",
        "n = 10  # Number of nodes\n",
        "p = 0.3  # Probability of edge creation\n",
        "G = nx.erdos_renyi_graph(n, p)\n",
        "\n",
        "# Calculate the k-core decomposition\n",
        "core_number = nx.core_number(G)\n",
        "\n",
        "# Visualize the network graph\n",
        "pos = nx.spring_layout(G)\n",
        "nx.draw_networkx_nodes(G, pos, node_color='lightblue', node_size=500)\n",
        "nx.draw_networkx_edges(G, pos, edge_color='gray')\n",
        "nx.draw_networkx_labels(G, pos, font_color='black', font_size=10)\n",
        "plt.title('Random Network Visualization')\n",
        "plt.axis('off')\n",
        "plt.show()\n",
        "\n",
        "# Print the core number of each node\n",
        "print('Node\\tCore Number')\n",
        "for node, core in core_number.items():\n",
        "    print(f'{node}\\t\\t{core}')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 624
        },
        "id": "b5uaxG-v2Ya5",
        "outputId": "c8e6ade5-4950-4a7c-a993-021f20aea04f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Node\tCore Number\n",
            "0\t\t2\n",
            "1\t\t1\n",
            "2\t\t2\n",
            "3\t\t1\n",
            "4\t\t2\n",
            "5\t\t2\n",
            "6\t\t2\n",
            "7\t\t2\n",
            "8\t\t2\n",
            "9\t\t2\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import networkx as nx\n",
        "import numpy as np\n",
        "import os\n",
        "import matplotlib.pyplot as plt\n",
        "from google.colab import drive\n",
        "\n",
        "# Mount Google Drive\n",
        "drive.mount('/content/gdrive')\n",
        "\n",
        "num_samples = 20\n",
        "num_nodes = 100\n",
        "p = 0.2\n",
        "\n",
        "network_properties = {\n",
        "    'k-core range': nx.core_number\n",
        "}\n",
        "\n",
        "# Create a directory to save the generated networks\n",
        "save_directory = '/content/gdrive/My Drive/generated_networks'\n",
        "os.makedirs(save_directory, exist_ok=True)\n",
        "\n",
        "results = {}\n",
        "\n",
        "for i in range(num_samples):\n",
        "    # Generate Erdos-Renyi graph\n",
        "    G = nx.erdos_renyi_graph(num_nodes, p)\n",
        "\n",
        "    # Save the generated network\n",
        "    save_path = os.path.join(save_directory, f'er_sample_{i}.gml')\n",
        "    nx.write_gml(G, save_path)\n",
        "\n",
        "    # Visualize the graph\n",
        "    plt.figure(figsize=(6, 4))\n",
        "    pos = nx.spring_layout(G)\n",
        "    nx.draw(G, pos, with_labels=True, node_color='lightblue', node_size=200, edge_color='gray')\n",
        "    plt.title(f'Erdos-Renyi Graph Sample {i}')\n",
        "    plt.savefig(os.path.join(save_directory, f'er_sample_{i}.png'))\n",
        "    plt.close()\n",
        "\n",
        "    # Calculate k-core range\n",
        "    kcore_range = nx.core_number(G)\n",
        "    kcore_values = list(kcore_range.values())\n",
        "    min_kcore = min(kcore_values)\n",
        "    max_kcore = max(kcore_values)\n",
        "\n",
        "    results[f'sample_{i}'] = {\n",
        "        'min_kcore': min_kcore,\n",
        "        'max_kcore': max_kcore\n",
        "    }\n",
        "\n",
        "# Print results\n",
        "print('K-Core Range for Erdos-Renyi Graphs:')\n",
        "for sample, kcore_range in results.items():\n",
        "    print(f'{sample}:')\n",
        "    print(f'  Min K-Core: {kcore_range[\"min_kcore\"]}')\n",
        "    print(f'  Max K-Core: {kcore_range[\"max_kcore\"]}')\n",
        "    print('')\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "R_f8cZyWC-0L",
        "outputId": "2c5700cf-e6b6-4031-96af-3fe9ec30758d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mounted at /content/gdrive\n",
            "K-Core Range for Erdos-Renyi Graphs:\n",
            "sample_0:\n",
            "  Min K-Core: 9\n",
            "  Max K-Core: 14\n",
            "\n",
            "sample_1:\n",
            "  Min K-Core: 12\n",
            "  Max K-Core: 15\n",
            "\n",
            "sample_2:\n",
            "  Min K-Core: 13\n",
            "  Max K-Core: 14\n",
            "\n",
            "sample_3:\n",
            "  Min K-Core: 12\n",
            "  Max K-Core: 14\n",
            "\n",
            "sample_4:\n",
            "  Min K-Core: 9\n",
            "  Max K-Core: 14\n",
            "\n",
            "sample_5:\n",
            "  Min K-Core: 11\n",
            "  Max K-Core: 15\n",
            "\n",
            "sample_6:\n",
            "  Min K-Core: 11\n",
            "  Max K-Core: 14\n",
            "\n",
            "sample_7:\n",
            "  Min K-Core: 12\n",
            "  Max K-Core: 15\n",
            "\n",
            "sample_8:\n",
            "  Min K-Core: 10\n",
            "  Max K-Core: 14\n",
            "\n",
            "sample_9:\n",
            "  Min K-Core: 9\n",
            "  Max K-Core: 15\n",
            "\n",
            "sample_10:\n",
            "  Min K-Core: 13\n",
            "  Max K-Core: 14\n",
            "\n",
            "sample_11:\n",
            "  Min K-Core: 12\n",
            "  Max K-Core: 14\n",
            "\n",
            "sample_12:\n",
            "  Min K-Core: 9\n",
            "  Max K-Core: 14\n",
            "\n",
            "sample_13:\n",
            "  Min K-Core: 10\n",
            "  Max K-Core: 14\n",
            "\n",
            "sample_14:\n",
            "  Min K-Core: 10\n",
            "  Max K-Core: 14\n",
            "\n",
            "sample_15:\n",
            "  Min K-Core: 12\n",
            "  Max K-Core: 15\n",
            "\n",
            "sample_16:\n",
            "  Min K-Core: 8\n",
            "  Max K-Core: 14\n",
            "\n",
            "sample_17:\n",
            "  Min K-Core: 11\n",
            "  Max K-Core: 15\n",
            "\n",
            "sample_18:\n",
            "  Min K-Core: 12\n",
            "  Max K-Core: 14\n",
            "\n",
            "sample_19:\n",
            "  Min K-Core: 9\n",
            "  Max K-Core: 15\n",
            "\n"
          ]
        }
      ]
    }
  ],
  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyMcI10XjuceicOS08khylBB",
      "include_colab_link": true
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}