{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Pagerank\n",
    "\n",
    "## Graphs\n",
    "We can use the networkx library to store and manipulate graphs in python"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 210,
   "metadata": {},
   "outputs": [],
   "source": [
    "import networkx as nx\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "myedges = [(0,1),(2,1),(3,0),(4,5),(5,0),(0,6),(1,5),(1,6),(2,4),(3,2),(4,3),(3,7),(4,7),(5,7),(6,3),(6,4),(6,5),(7,1),(7,6)]\n",
    "\n",
    "G = nx.DiGraph() ## Directed Graph\n",
    "G.add_edges_from(myedges)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 231,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw(G)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are a lot of options you can use to display graphs with networkx "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 240,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw(G, pos=nx.circular_layout(G), with_labels = True, width = 1.5, node_color=\"lightblue\", node_size = 1000, arrowstyle=\"-|>\", arrowsize=15 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 241,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 241,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Get the outgoing degree of a vertex\n",
    "G.out_degree(6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 242,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[3, 4, 5]"
      ]
     },
     "execution_count": 242,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(G.successors(6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 243,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 1, 2, 3, 4, 5, 6, 7]"
      ]
     },
     "execution_count": 243,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(G.nodes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 246,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 246,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "random.choice(list(G.successors(6)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulate a random websurfer\n",
    "One way to rank the nodes is to simulate a random walk on the graph.  Choose an initial vertex.  Then randomly follow an outgoing edge to another vertex.  Do this many times and count the proportion of time you spend at each vertex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 249,
   "metadata": {},
   "outputs": [],
   "source": [
    "def websim(graph, iterations):\n",
    "    vertices = list(G.nodes)\n",
    "    vertexcount = np.zeros(len(vertices))\n",
    "    currentvertex = random.choice(vertices)\n",
    "    for i in range(iterations):\n",
    "        newvertex = random.choice(list(G.successors(currentvertex)))\n",
    "        currentvertex = newvertex\n",
    "        vertexcount[currentvertex]+=1\n",
    "    return 1/iterations * vertexcount\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 250,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.11781  0.14749  0.032317 0.09685  0.084756 0.170122 0.205501 0.145154]\n"
     ]
    }
   ],
   "source": [
    "weights = websim(G,1000000)\n",
    "print(weights)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pagerank"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another way is to rank each vertex with a rank with the property that the rank $r_i$ of vertex $i$ is given by the sume $$r_i = \\sum \\frac{r_j}{d_j}$$\n",
    "where the sum is over each vertex $j$ for which there is an edge $j \\to i$ and $d_j$ is the outgoing degree of vertex $j$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is convenient to use the built in adjacency matrix function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 251,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/yv/0wjzc10d30z52y56qczm8s5c0000gp/T/ipykernel_66848/1018844737.py:1: FutureWarning: adjacency_matrix will return a scipy.sparse array instead of a matrix in Networkx 3.0.\n",
      "  A = nx.adjacency_matrix(G)\n"
     ]
    }
   ],
   "source": [
    "A = nx.adjacency_matrix(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 252,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<8x8 sparse matrix of type '<class 'numpy.int64'>'\n",
       "\twith 19 stored elements in Compressed Sparse Row format>"
      ]
     },
     "execution_count": 252,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "nx.adjacency_matrix returns a sparse matrix.  You can get a dense matrix if desired."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 255,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[0, 1, 0, 0, 0, 0, 1, 0],\n",
       "        [0, 0, 0, 0, 0, 1, 1, 0],\n",
       "        [0, 1, 0, 0, 1, 0, 0, 0],\n",
       "        [1, 0, 1, 0, 0, 0, 0, 1],\n",
       "        [0, 0, 0, 1, 0, 1, 0, 1],\n",
       "        [1, 0, 0, 0, 0, 0, 0, 1],\n",
       "        [0, 0, 0, 1, 1, 1, 0, 0],\n",
       "        [0, 1, 0, 0, 0, 0, 1, 0]])"
      ]
     },
     "execution_count": 255,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.todense()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 254,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = A.todense()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[0, 1, 0, 0, 0, 0, 1, 0],\n",
       "        [0, 0, 0, 0, 0, 1, 1, 0],\n",
       "        [0, 1, 0, 0, 1, 0, 0, 0],\n",
       "        [1, 0, 1, 0, 1, 0, 0, 1],\n",
       "        [0, 0, 0, 0, 0, 1, 0, 1],\n",
       "        [1, 0, 0, 0, 0, 0, 0, 1],\n",
       "        [0, 0, 0, 1, 1, 1, 0, 0],\n",
       "        [0, 1, 0, 0, 0, 0, 1, 0]])"
      ]
     },
     "execution_count": 193,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[1, 0, 1, 0, 1, 0, 0, 1]])"
      ]
     },
     "execution_count": 194,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is a 1 in row i, column j if there is a directed edge starting at vertex i and terminating at vertex j.  So, the entry \"1\" in the second row, sixth column is there because there is an edge from the second vertex to the sixth vertex (vertex 1 to vertex 5, since we started counting at 0)\n",
    "\n",
    "For the pagerank algorithm, we'd like a matrix with the entry $\\frac{1}{d_j}$ in the i-th row and j-th column if there is an edge from vertex j to vertex i, and vertex j has d outgoing edges. \n",
    "\n",
    "We can determine the number of outgoing edges for each vertex:  The number of edges coming out of vertex i is the total number of 1's in row i.  For example, the number edges originating at vertex 7 is "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 256,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(8, 8)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 256,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(np.shape(a))\n",
    "np.sum(a[6])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 257,
   "metadata": {},
   "outputs": [],
   "source": [
    "n,k = np.shape(a)\n",
    "d = [np.sum(a[i]) for i in range(n)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 259,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2, 2, 2, 3, 3, 2, 3, 2]\n"
     ]
    }
   ],
   "source": [
    "print(d) # the outgoing degrees of each vertex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 260,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.         0.         0.         0.33333333 0.         0.5\n",
      "  0.         0.        ]\n",
      " [0.5        0.         0.5        0.         0.         0.\n",
      "  0.         0.5       ]\n",
      " [0.         0.         0.         0.33333333 0.         0.\n",
      "  0.         0.        ]\n",
      " [0.         0.         0.         0.         0.33333333 0.\n",
      "  0.33333333 0.        ]\n",
      " [0.         0.         0.5        0.         0.         0.\n",
      "  0.33333333 0.        ]\n",
      " [0.         0.5        0.         0.         0.33333333 0.\n",
      "  0.33333333 0.        ]\n",
      " [0.5        0.5        0.         0.         0.         0.\n",
      "  0.         0.5       ]\n",
      " [0.         0.         0.         0.33333333 0.33333333 0.5\n",
      "  0.         0.        ]]\n"
     ]
    }
   ],
   "source": [
    "c = np.array([[1/d[j]* a[j, i] for j in range(n)] for i in range(n)])\n",
    "print(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 261,
   "metadata": {},
   "outputs": [],
   "source": [
    "eigenvalues, eigenvectors = np.linalg.eig(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 262,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.00000000e+00+0.j        , -2.70514331e-01+0.76370066j,\n",
       "       -2.70514331e-01-0.76370066j, -3.07828932e-01+0.21757611j,\n",
       "       -3.07828932e-01-0.21757611j,  7.83432628e-02+0.20855756j,\n",
       "        7.83432628e-02-0.20855756j, -9.79174615e-17+0.j        ])"
      ]
     },
     "execution_count": 262,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eigenvalues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 267,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.3078325 +0.j, -0.38698943+0.j, -0.08443406+0.j, -0.25330217+0.j,\n",
       "       -0.2216394 +0.j, -0.44679688+0.j, -0.53826711+0.j, -0.3817123 +0.j])"
      ]
     },
     "execution_count": 267,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eigenvectors[:,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 268,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mypowermethod(A, y, n):\n",
    "  for i in range(n):\n",
    "    y =  np.dot(A,y)\n",
    "    y = 1/ np.linalg.norm(y)*y\n",
    "  return y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 269,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.14058692  0.64107577  0.30461388  0.72064268 -0.93439056  0.33711978\n",
      " -0.55560189 -0.3537261 ]\n"
     ]
    }
   ],
   "source": [
    "initv = np.ones(n)-2*np.random.rand(8)\n",
    "print(initv)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 270,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.30783249 0.38698948 0.08443406 0.25330214 0.22163938 0.44679684\n",
      " 0.53826714 0.38171229]\n"
     ]
    }
   ],
   "source": [
    "weights2 = mypowermethod(c,initv,100)\n",
    "print(weights2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 271,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.30783247, 0.38698942, 0.08443405, 0.25330217, 0.22163941,\n",
       "       0.44679691, 0.53826713, 0.38171226])"
      ]
     },
     "execution_count": 271,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(c,weights2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 276,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.11744966, 0.14765103, 0.03221477, 0.09664429, 0.08456375,\n",
       "       0.17046978, 0.20536914, 0.14563758])"
      ]
     },
     "execution_count": 276,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weights2 / np.sum(weights2) # scale so the sum is 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 277,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.11761 0.14532 0.0328  0.09839 0.08526 0.16853 0.20712 0.14497]\n"
     ]
    }
   ],
   "source": [
    "weights = websim(G,100000)\n",
    "print(weights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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