Page_Rank.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Page Rank.ipynb",
      "provenance": [],
      "authorship_tag": "ABX9TyMdQp+Y8Lc8h4RcvlRILYjG",
      "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/bhartimeena/Assingment/blob/main/Page_Rank.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "z_Y5r38Fsv_r"
      },
      "source": [
        "from google.colab import drive\n",
        "import numpy as np\n",
        "from scipy.sparse import dok_matrix\n",
        "import networkx as nx\n"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-A-5L4pvsx-v",
        "outputId": "cdc994dd-4303-4604-a1f1-506795c60548"
      },
      "source": [
        "drive.mount('/content/drive')"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mounted at /content/drive\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KT5HxB9Os2pG"
      },
      "source": [
        "% cd /content/drive/MyDrive/Colab Notebooks/Page Rank/\n",
        "% ls\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "wonC47Uys5wL",
        "outputId": "70704ef1-f07b-4fcb-fbb0-1be26301c216"
      },
      "source": [
        "# Now , here I will try to show the sparse matrix looks like and also showing the small prototype of the graph made out of the nodes and the edges ...\n",
        "# Since , drawing the graph for the original dataset won't be possible as the collab session times out after 1 hr. in my PC , ad also it shows the estimated time to be around 5 hr .\n",
        "\n",
        "A = np.array([\n",
        "  [0, 0, 1, 1],\n",
        "  [1, 0, 1, 0],\n",
        "  [1, 1, 0, 1],\n",
        "  [1, 1, 1, 0],\n",
        "])\n",
        "A = A/np.sum(A, axis=0)\n",
        "v = np.array([1, 1, 1, 1])\n",
        "v = v/np.sum(v)\n",
        "v = v.reshape((4, 1))\n",
        "A\n"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.        , 0.        , 0.33333333, 0.5       ],\n",
              "       [0.33333333, 0.        , 0.33333333, 0.        ],\n",
              "       [0.33333333, 0.5       , 0.        , 0.5       ],\n",
              "       [0.33333333, 0.5       , 0.33333333, 0.        ]])"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 319
        },
        "id": "CUvFR2S_s8_Z",
        "outputId": "c35e74a8-dcba-4ea0-d6af-8105db3dfed9"
      },
      "source": [
        "G = nx.DiGraph()\n",
        "for ii, i in enumerate(A):\n",
        "  for jj, j in enumerate(i):\n",
        "    if j>0:\n",
        "      G.add_edge(ii, jj, weight=j)\n",
        "nx.draw(G, with_labels=True)"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5c_cG7oatAVU",
        "outputId": "5b354ab5-8562-4aa8-c032-e9172b6250fa"
      },
      "source": [
        "print(\"Nodes are : \" ,list(G.nodes))\n",
        "print(\"Edges are : \" ,list(G.edges))\n"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Nodes are :  [0, 2, 3, 1]\n",
            "Edges are :  [(0, 2), (0, 3), (2, 0), (2, 1), (2, 3), (3, 0), (3, 1), (3, 2), (1, 0), (1, 2)]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "g1F7vcU5twiS"
      },
      "source": [
        "# Now the actual code for the page rank starts ......\n",
        "# So , now from the web Standford.txt file , we perform the page ranking \n",
        "G = nx.DiGraph()\n",
        "dims = 281903 # because these are these many of the nodes which hase been printed below..\n",
        "sparse_matrix = dok_matrix((dims, dims), dtype=np.float32)\n",
        "D = np.zeros(dims)\n",
        "\n",
        "with open('web-Stanford.txt', 'r') as f:\n",
        "  # skipping first 4 comments, as these details are not required for the page rank algorithm ..\n",
        "  for i in range(4):\n",
        "    next(f)\n",
        "  for i in f:\n",
        "    start_node, end_node = list(map(int, i.split()))\n",
        "    G.add_edge(start_node, end_node)\n",
        "    D[start_node-1] = D[start_node-1] + 1\n",
        "\n",
        "with open('web-Stanford.txt', 'r') as f:\n",
        "  # skipping first 4 comments, can be done by putting condition of '#'and also as these details are not required for the page rank algorithm\n",
        "  for i in range(4):\n",
        "    next(f)\n",
        "  for i in f:\n",
        "    start_node, end_node = list(map(int, i.split()))\n",
        "    sparse_matrix[start_node-1, end_node-1] = 1/D[start_node-1]\n",
        "sparse_matrix = sparse_matrix.tocsr()\n",
        "\n",
        "print(sparse_matrix)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9L0HFV7cuAUF"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Z5PwF1Ltt32g",
        "outputId": "7405a0bc-0a60-439c-993d-e7e553997a48"
      },
      "source": [
        "print(\"Total Nodes : \" ,len(list(G.nodes)))\n",
        "print(\"Total Edges : \" ,len(list(G.edges)))\n",
        "# nx.draw(G, with_labels=True)"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Total Nodes :  0\n",
            "Total Edges :  0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tDmJgIUguB77"
      },
      "source": [
        "def get_ranks(H, v, N, dangling_factor=0.85):\n",
        "  iters = 0\n",
        "  while True:\n",
        "    new_v = dangling_factor * (H @ v) + (1-dangling_factor)/N\n",
        "    \n",
        "    iters+=1\n",
        "    if np.allclose(new_v, v):\n",
        "      break\n",
        "    v = new_v\n",
        "  print(iters)\n",
        "  print(v)\n",
        "  return v\n",
        "v = np.ones(dims)/dims\n",
        "z = get_ranks(sparce_matrix, v, dims)\n",
        "\n",
        "# Over here we have taken the default value of the Damping factor to be 0.85 and then this function is going to return the rank of the pages or documents.\n",
        "# We are returning the the iteration taken and also the the vector V finally ."
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TBnHYCnJuGzf"
      },
      "source": [
        "# checking if the sum of the probabilities is close to 1 or not ..\n",
        "np.sum(z)\n"
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}