pagerank.ipynb

pagerank.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# similarity matrix\n",
    "S = np.array([[0,1,1,1,0],\n",
    "              [1,0,1,0,0],\n",
    "              [1,1,0,1,1],\n",
    "              [1,0,1,0,1],\n",
    "              [0,0,1,1,0]])\n",
    "\n",
    "n = S.shape[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# normalize columns\n",
    "B = S / np.sum(S, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# damping coefficient\n",
    "c = 0.85"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.03       0.455      0.2425     0.31333333 0.03      ]\n",
      " [0.31333333 0.03       0.2425     0.03       0.03      ]\n",
      " [0.31333333 0.455      0.03       0.31333333 0.455     ]\n",
      " [0.31333333 0.03       0.2425     0.03       0.455     ]\n",
      " [0.03       0.03       0.2425     0.31333333 0.03      ]]\n"
     ]
    }
   ],
   "source": [
    "# pagerank matrix\n",
    "A = c * B + (1 - c) * np.full((n, n), 1 / n)\n",
    "\n",
    "print(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 1., 1., 1., 1.])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# confirm that A is normalized\n",
    "np.sum(A, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "w, v = np.linalg.eig(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1.          0.2331481  -0.14166667 -0.51648144 -0.425     ]\n"
     ]
    }
   ],
   "source": [
    "# eigenvalues\n",
    "print(w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.46193615 0.32416572 0.60254721 0.46193615 0.32416572]\n"
     ]
    }
   ],
   "source": [
    "# dominant eigenvector\n",
    "print(np.abs(v[:,0]))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}