Graph_Q8.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyO+RBnMw0+rW2qZ29r0eaWV",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/nawidadkhah/Graph_Simulation/blob/main/Graph_Q8.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import networkx as nx\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "import math\n",
        "import random\n",
        "import matplotlib.pyplot as plt"
      ],
      "metadata": {
        "id": "aIib0R02e6uW"
      },
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "9myLqDTSeywp",
        "outputId": "859746cc-603a-4f28-c1e3-d1f1e408a789"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# Q8-Part1: Exponential Life Time\n",
        "n = 100\n",
        "r = 2\n",
        "k = 4\n",
        "exp_times = list()\n",
        "\n",
        "for _ in range(1000):\n",
        "  nodes_q8 = list()\n",
        "  for i in range(n):\n",
        "    t = np.random.exponential()\n",
        "    nodes_q8.append(t)\n",
        "\n",
        "  g = nx.random_regular_graph(k, n)\n",
        "\n",
        "  passed_time = 0.0\n",
        "  for i in range(200):\n",
        "\n",
        "    for j in range(len(nodes_q8)):\n",
        "      if j >= len(nodes_q8):\n",
        "        continue\n",
        "      if g.has_node(j) is False:\n",
        "        continue\n",
        "      if nodes_q8[j] <= passed_time:\n",
        "        g.remove_node(j)\n",
        "        nodes_q8.pop(j)\n",
        "\n",
        "    degrees_g = [g.degree(n) for n in g.nodes()]\n",
        "    if r in degrees_g:\n",
        "      exp_times.append(passed_time)\n",
        "      break\n",
        "\n",
        "    passed_time += 0.01\n",
        "\n",
        "\n",
        "plt.hist(exp_times, color='cyan')\n",
        "plt.title(\"Time for Isolation in Exponential Life Time\")\n",
        "plt.xlabel(\"Time to Isolation\")\n",
        "plt.ylabel(\"Number of the Graphs\")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Q8-Part2: Weibull Life Time\n",
        "n = 100\n",
        "r = 2\n",
        "k = 4\n",
        "exp_times = list()\n",
        "\n",
        "for _ in range(1000):\n",
        "  nodes_q8 = list()\n",
        "  for i in range(n):\n",
        "    t = np.random.weibull(3)\n",
        "    nodes_q8.append(t)\n",
        "\n",
        "  g = nx.random_regular_graph(k, n)\n",
        "\n",
        "  passed_time = 0.0\n",
        "  for i in range(200):\n",
        "\n",
        "    for j in range(len(nodes_q8)):\n",
        "      if j >= len(nodes_q8):\n",
        "        continue\n",
        "      if g.has_node(j) is False:\n",
        "        continue\n",
        "      if nodes_q8[j] <= passed_time:\n",
        "        g.remove_node(j)\n",
        "        nodes_q8.pop(j)\n",
        "\n",
        "    degrees_g = [g.degree(n) for n in g.nodes()]\n",
        "    if r in degrees_g:\n",
        "      exp_times.append(passed_time)\n",
        "      break\n",
        "\n",
        "    passed_time += 0.01\n",
        "\n",
        "\n",
        "plt.hist(exp_times, color='green')\n",
        "plt.title(\"Time for Isolation in Weibull Life Time\")\n",
        "plt.xlabel(\"Time to Isolation\")\n",
        "plt.ylabel(\"Number of the Graphs\")\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "c8EAtmQrfFOi",
        "outputId": "1c7ea0b8-b425-4f97-9593-a716feff409c"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Q8-Part3: Pareto Life Time\n",
        "n = 100\n",
        "r = 2\n",
        "k = 4\n",
        "exp_times = list()\n",
        "\n",
        "for _ in range(1000):\n",
        "  nodes_q8 = list()\n",
        "  for i in range(n):\n",
        "    t = np.random.pareto(1)\n",
        "    nodes_q8.append(t)\n",
        "\n",
        "  g = nx.random_regular_graph(k, n)\n",
        "\n",
        "  passed_time = 0.0\n",
        "  for i in range(200):\n",
        "\n",
        "    for j in range(len(nodes_q8)):\n",
        "      if j >= len(nodes_q8):\n",
        "        continue\n",
        "      if g.has_node(j) is False:\n",
        "        continue\n",
        "      if nodes_q8[j] <= passed_time:\n",
        "        g.remove_node(j)\n",
        "        nodes_q8.pop(j)\n",
        "\n",
        "    degrees_g = [g.degree(n) for n in g.nodes()]\n",
        "    if r in degrees_g:\n",
        "      exp_times.append(passed_time)\n",
        "      break\n",
        "\n",
        "    passed_time += 0.01\n",
        "\n",
        "\n",
        "plt.hist(exp_times, color='red')\n",
        "plt.title(\"Time for Isolation in Pareto Life Time\")\n",
        "plt.xlabel(\"Time to Isolation\")\n",
        "plt.ylabel(\"Number of the Graphs\")\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "uvmBhCg0fKOx",
        "outputId": "55cf6203-8f22-4075-a8d6-0e7ef5cb9426"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    }
  ]
}