{ "cells": [ { "cell_type": "markdown", "id": "da51a270", "metadata": {}, "source": [ "# TP - PageRank\n", "\n", "Le but de cette séance est d’implémenter l’algorithme de puissance itérée pour pouvoir ensuite calculer la centralité de vecteur propre dans le cas des graphes non orientés et également dans le des graphes orientés (Page Rank).\n", "Nous utiliserons le module `networksx` de Python.\n", "\n", "Pour l'ensemble des graphes que nous allons manipuler dans ce TP, il faut que les sommets soient obligatoirement numéroté de $0$ à $n-1$." ] }, { "cell_type": "code", "execution_count": 6, "id": "aa58658e", "metadata": {}, "outputs": [], "source": [ "import networkx as nx\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import scipy as sp\n", "import time\n", "import math" ] }, { "cell_type": "markdown", "id": "a1899515", "metadata": {}, "source": [ "## Quelques fonctions utiles" ] }, { "cell_type": "code", "execution_count": 7, "id": "959dce47", "metadata": {}, "outputs": [], "source": [ "# Return the adjacency matrix of G as list of lists\n", "def adjacencyMatrix(G):\n", " return nx.to_numpy_array(G, nodelist=range(len(G))) #nx.adjacency_matrix(G).todense()\n", "\n", "# Return the matrix product of A and B\n", "def multMatrix(A,B):\n", " return A.dot(B)\n", "\n", "# Return the same graph as G whose vertices are relabeled from 0 to n-1\n", "# and the mapping (old:new) names\n", "def relabelGraph(G):\n", " mapping = dict(zip(G, range(0, len(G))))\n", " return nx.relabel_nodes(G, mapping), mapping \n", "\n", "# Return original name of the vertex from new name\n", "def getOriginalName(mapping, v):\n", " return [k for k,u in mapping.items() if u == v][0]\n", "\n", "# Draw the graph G. If a centrality measure is given in C, label the vertices. \n", "# Different layouts can be used: neato (default), fdp, patchwork, circo, ... List of layout : https://graphviz.org/docs/layouts/\n", "def drawGraph(G,C=None,prog=\"neato\"):\n", " pos=nx.nx_agraph.pygraphviz_layout(G,prog=prog) # Position of vertices\n", " node_size=[300 for _ in G] # default size of nodes\n", " with_labels=True\n", " if C is not None: # if a centrality measure is given, label the vertices\n", " with_labels=False\n", " labels_nodes = {v:C[v][0] for v in G}\n", " max_C=max(C)[0]\n", " node_size=[math.exp(labels_nodes[v]*7/max_C) for v in labels_nodes] # size the vertices depending on the centrality measure\n", " nx.draw_networkx_labels(G,pos,labels_nodes,font_size=12,font_color=\"black\") # draw labels\n", " nx.draw(G,pos=pos,node_size=node_size,with_labels = with_labels) # draw graph\n", " plt.show() " ] }, { "cell_type": "markdown", "id": "f09fc42f", "metadata": {}, "source": [ "## Quelques graphes pour faire des tests\n", "\n", "1. Un premier exemple de graphe non orienté à 4 sommets :" ] }, { "cell_type": "code", "execution_count": 8, "id": "58fda754", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Matrice d'adjacence du graphe G1: \n", " [[0. 1. 1. 1.]\n", " [1. 0. 1. 0.]\n", " [1. 1. 0. 0.]\n", " [1. 0. 0. 0.]]\n" ] }, { "data": { "image/png": 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74wBAwaijog4FXTrqqF69ekXu1QwPD2fUEXwehRIe5bvvvlPr1q01Y8YMDRo0yO44AHBVp0+fvqxoJiUlaffu3crLy5P081FHly6hN2rUiFFH8BkUSnictm3bqnbt2po1a5bdUQDgpuTm5mrv3r2XFc2dO3cWOeqo8F5NRh3B21Ao4XE+/vhj/fa3v9XBgwcVHh5udxwAKDaFRx1denXzxx9//Nmoo6LuFMSoI3gqCiU8zpkzZxQeHq4XXnhBf/nLX+yOAwCl4sKFC0pJSbmsaBYeddSoUaPLiiajjmA3CiU80v33368NGzYoOTmZzewA/NrFUUdFHQq6dNRRrVq1ijwUVK9ePUYdocRRKOGRVqxYoe7du2vFihW666677I4DAB4pIyOjYNTRpT+uNuroYtFs0qQJt7pFsaFQwiNZlqUmTZqoQ4cO+uqrr+yOAwBexeVy6cCBA0UOcE9LSyt43MVRR4X3azLq6Oosy9Kh01n68cR55bjyFRoUoIbVyiq8Yqjf/n+jUMJjvfbaa3rppZeUmprK3iAAKCaFRx1d/HlRo44KF01/HnVkWZbW7z2przfs1+qUE8rIzrvsMRXDgtS9aXXd376+7qhX2a/KJYUSHuvIkSOqW7euPvzwQz366KN2xwEAn3bpqKNLC2fhUUe33HLLZYeCfH3U0bZDZ/T0lO+UfCxDAU6HXPlXrk4Xv397REW9PayVGtcsX4pJ7UOhhEcbOHCgjh49qsTERLujAIBfujjqqKhDQZeOOqpSpUqRp88bNmzotaOOLMvSe0tT9MGyFDkkuW6gMQU4HXJI+kvfZhrT6Rafv1pJoYRHmzFjhgYPHqytW7eqVatWdscBAFziwoUL2r1792VFMykpSRkZGZIuH3V0cRm9adOmqlSpkr0f4Cosy9JfE7YrPvGg26/1m26R+lOfZsWQynNRKOHRcnNzVbduXQ0fPlzvv/++3XEAANfBsiwdOXKkyKJ58OD/F7SLo44K79X0hFFH7y9N0TtLkovt9V4a1EL3t69fbK/naSiU8Hh/+tOfNH78eB05ckShoaF2xwEAuKHwqKOLS+lJSUkFo45CQ0N/Nuro4o/SGnX0/ZGzuvffa3SlrZL5OVlK3zhd2UeSlJOarPwLGara70mVu73XFV8zJNCpRU92Vf2qvjmqiUIJj5eUlKRmzZopPj5eI0eOtDsOAKAEFB51dOmezUtHHdWtW7fIvZq1a9culn2KlmWp3werlZyWccXDN3ln0nR43BgFVKiuwEq1lH1g+zULZYDToQ4NqypuTLTbGT0RhRJeoUuXLgoNDdXixYvtjgIAKGUXRx0VPhh06aijcuXKFVk0GzdufEOjjhL3ndKwT9Zf9TFWXq7yL2QooFxlZaem6OiXT12zUF605KmualTD905+e+exK/idMWPG6Je//KX27dunBg0a2B0HAFCKKleurPbt26t9+/Y/+3pubq5+/PHHy/Zqzp07V6dPn5Z0+aijS/drVqtW7bKrmnEb9l9zNJAjMEgB5Srf8OcIcDpkbjygFwbedsPP9XRcoYRXOH/+vMLDw/XUU0/pxRdftDsOAMCDWZalEydOFHmnoB9//FH5+fmS/n/U0aUl87lvg3X2guu63+tGr1A2qlFOS57yvVsKUyjhNR555BHNnz9f+/btU0BAgN1xAABeqPCoo0uX0TOtQNX9bdwNvd6NFkqnQ9rx4j0KDfKtv8dY8obXGDNmjP7zn/9o8eLFuueee+yOAwDwQqGhoWrRooVatGjxs69blqUFW5L162m7S/T98y3p0OksNapRrkTfp7TZO+QJuAHt2rXTbbfdps8++8zuKAAAH+NwOFSxctVSea9cV36pvE9polDCazgcDj388MOaOXOmjh8/bnccAICPKa1l6DAfW+6WKJTwMrGxsZKkuLgb2+MCAMC1RFYv+WXooACHIiqHlfj7lDYKJbxKtWrVdN999+mzzz4T58kAAMWpYliQapUPLtH3aFargoICfK9+cSgHXmfMmDG65557tGnTJkVH++YdBwAApef8+fOaNWuWTNPU7rx6KtvqHjmcV1+WTt8yW/kXzsuVcUqSlLV7k/LOnZAkVbhzoJyhl99i0emQejSrUfwfwANQKOF1evXqpbp162r8+PEUSgDATcnLy9PSpUsVFxenhIQEnT9/Xh07dtTvhg/S50evvccxfWOCXOnHCv47M3mdlLxOklTutu5FFkpJGhVVr3g+gIdhDiW80gsvvKB33nlHqampKlfOt0YvAABKhmVZSkxMlGmamjhxoo4dO6ZmzZopNjZWo0eP1i233CJJ+sXnm7Rmz4mr3i3nRgU4HBrYqrbeG9G62F7Tk1Ao4ZX27dunhg0b6rPPPtMvf/lLu+MAADxYSkqKTNPUhAkTlJKSovDwcI0aNUqGYahNmzaX3X7x8Jks9XpnpbJyr/+OOVfj0P/2Zy77QzdVKVuyezTtQqGE1+rdu7cyMzO1Zs0au6MAADxMWlqaJk2aJNM0tWnTJpUvX14xMTEyDEPdunW75h3Xpn9zSL+f8l2xZHFIGv9AW/W8tWaxvJ4nYg8lvNaYMWM0cuRI7dq1S82aNbM7DgDAZhkZGZoxY4bi4uK0ZMkSOZ1O9evXT5MnT9aAAQMUFnb943qG3FFHpzNz9dLcHXJIupmrb46fnvjPmFY+XSYlrlDCi2VnZ6t27doaM2aM3nzzTbvjAABskJubq0WLFsk0Tc2cOVOZmZnq0qWLYmNjFRMToypVqrj1+rO3HdEz07crK9d1Q3sqAxwOVQwL0tvDWqm7j57svhSFEl7tiSee0MSJE3Xo0CEFBQXZHQcAUAosy9L69etlmqYmT56sEydOqEWLFjIMQ6NGjVL9+vWL9f2OpV/Qi3N2aP73qZL+dz/uK3E6/ndnt6FtIvTXfreqUhnf3DNZGIUSXm3btm1q1aqVpk+frsGDB9sdBwBQgnbt2lVwuGbv3r2qU6eORo8eLcMwdPvtt5f4+6eezdLExINalXJcO46kKzvv/+/JHRYcoBa1K6hb0xoa0bauqpULKfE8noRCCa8XFRWlmjVras6cOXZHAQAUs9TUVE2cOFFxcXH65ptvVLFiRQ0bNkyGYahr165yOu2564wr39KxcxeU67IUEuhU9XIhcjod136ij6JQwuuNGzdOjz32mA4cOKCIiAi74wAA3JSenq7p06fLNE0tW7ZMgYGBGjBggGJjY9WvXz+FhPjX1T9v4Hs3k4TfGTVqlEJCQvTll1/aHQUAcJNycnI0a9YsDR8+XDVr1tRDDz0kl8ulTz/9VGlpaZo2bZoGDx5MmfRQXKGET/jFL36htWvXKjk52bblDwDAjcnPz9fatWtlmqamTJmiU6dOqVWrVgWHa+rUqWN3RFwnCiV8wqpVq3TXXXdp+fLl6tatm91xAABX8cMPPxQcrtm/f7/q169fcLjmtttuszsebgKFEj7Bsiw1bdpU0dHR+vrrr+2OAwAo5NChQ4qPj5dpmvruu+9UpUoVDRs2TLGxserYsSOrS16OQgmf8frrr+vFF19UamqqKlWqZHccAPB7Z86c0bRp0xQXF6eVK1cqJCRE9957rwzD0D333KPgYP+Y0egPKJTwGampqapbt67ef/99/eY3v7E7DgD4pezsbM2dO1emaWru3LnKzc1Vjx49ZBiGhgwZogoVKtgdESWAQgmfcu+99+rw4cPasmWL3VEAwG/k5+dr1apVBYdrzp49qzvvvFOGYWjkyJEKDw+3OyJKGIUSPmXWrFkaNGiQvv32W7Vu3druOADg07Zt26a4uDjFx8fr0KFDuuWWW2QYhgzDULNmzeyOh1JEoYRPycvLU926dRUTE6MPPvjA7jgA4HMOHDigCRMmyDRNff/996pWrZpGjBghwzDUvn17ORz+e7cYf0ahhM/5y1/+ok8//VRHjhxRaGio3XEAwOudOnVKU6ZMkWmaWr16tcLCwnTffffJMAz17t1bQUFBdkeEzSiU8DnJyclq2rSpJkyYoFGjRtkdBwC8UlZWlubMmSPTNDVv3jy5XC717t1bhmHovvvuU7ly5eyOCA9CoYRP6tq1q4KCgrR06VK7owCA13C5XFq+fLlM09S0adN07tw5tWvXToZhaMSIEapZs6bdEeGhKJTwSV9++aUefPBB7dmzRw0bNrQ7DgB4LMuy9O2338o0TcXHxys1NVWNGjVSbGysRo8ercaNG9sdEV6AQgmfdP78eYWHh+uJJ57QSy+9ZHccAPA4e/fuLThcs2vXLtWoUUMjR46UYRiKioricA1uCIUSPuvRRx/V3LlztW/fPgUEBNgdBwBsd+LECU2ePFmmaWrdunUqW7asBg8erNjYWPXs2VOBgYF2R4SXolDCZyUmJqpdu3aaN2+e+vbta3ccALBFZmamZs6cKdM0tXDhQklSnz59ZBiG7r33XpUtW9bmhPAFFEr4LMuy1KpVKzVp0kRTp061Ow4AlJq8vDwtXbpUpmkqISFBGRkZ6tChg2JjYzVs2DBVr17d7ojwMRRK+LR//etfevrpp3X48GHVqFHD7jgAUGIsy1JiYqJM09SkSZOUlpamZs2ayTAMjR49mgOKKFEUSvi0kydPqnbt2nr11Vf1hz/8we44AFDsdu/eLdM0ZZqmUlJSFB4erpEjRyo2NlZt2rThcA1KBYUSPm/EiBHavn27fvjhB/5gBeAT0tLSNGnSJJmmqU2bNql8+fIaOnSoDMNQ9+7dOYiIUkehhM9bvHixevfurXXr1qlDhw52xwGAm5KRkaEZM2bINE0tXrxYTqdTffv2VWxsrAYMGKCwsDC7I8KPUSjh8/Lz89WwYUP16tVL48ePtzsOAFy33NxcLVq0SKZpaubMmcrMzFSXLl1kGIZiYmJUtWpVuyMCkiiU8BMvvvii3nrrLaWmpnL/WQAezbIsbdiwoeBwzYkTJ3TbbbcVHK6pX7++3RGBy1Ao4RcOHDigBg0aaPz48XrooYfsjgMAl9m1a5dM09SECRO0d+9eRUREaPTo0TIMQ7fffjt7wOHRKJTwG3369NG5c+e0bt06u6MAgCQpNTVVEydOlGma2rJliypWrKiYmBgZhqGuXbtyuAZeg0IJvzF58mSNGDFCO3bs0K233mp3HAB+Kj09XQkJCYqLi9OyZcsUGBioAQMGyDAM9evXT6GhoXZHBG4YhRJ+Izs7WxEREXrwwQf11ltv2R0HgB/JycnRggULZJqmZs2apezsbN11110yDENDhw5V5cqV7Y4IuIVCCb/y1FNPyTRNHTp0SMHBwXbHAeDD8vPztW7dOsXFxWnKlCk6deqUWrVqJcMwNGrUKNWpU8fuiECxoVDCr3z//fdq2bKlpk2bpiFDhtgdB4AP+uGHHwoO1+zfv1/16tUrOFzTokULu+MBJYJCCb8THR2tatWqae7cuXZHAeAjDh8+rPj4eMXFxem7775T5cqVNXz4cBmGoU6dOsnpdNodEShRFEr4nU8//VS//vWvtX//fpacANy0M2fOaNq0aTJNUytWrFBISIgGDhwowzDUt29fttXAr/BPJvidkSNHKjQ0VF988YXdUQB4mezsbCUkJGjo0KGqVauWxo4dK6fTqc8//1xpaWmaPHmyBg0aRJmE3+EKJfzSgw8+qFWrVmn37t0sRQG4qvz8fK1atUqmaWrq1Kk6c+aM7rjjDhmGoZEjR6p27dp2RwRsR6GEX1q9erW6du2qpUuXqkePHnbHAeCBtm3bJtM0FR8fr4MHD+qWW24puP0hs2yBn6NQwi9ZlqVmzZqpbdu2Mk3T7jgAPMSBAwc0YcIEmaap77//XlWrVtWIESNkGIY6dOjA7Q+BK6BQwm+9+eabev7555WamspQYcCPnTp1SlOnTlVcXJxWr16tsLAwDRo0SLGxserdu7eCgoLsjgh4PAol/NbRo0dVp04d/etf/9Jjjz1mdxwApSgrK0tz5syRaZqaN2+eXC6X7r77bhmGofvuu0/ly5e3OyLgVSiU8Gv33XefDhw4oG+++cbuKABKmMvl0ooVK2SapqZNm6b09HRFRUUpNjZWI0aMUM2aNe2OCHgtCiX82uzZs3Xvvfdqy5YtuuOOO+yOA6CYWZalb7/9VqZpauLEiTpy5IgaNWpUcLimSZMmdkcEfAKFEn4tLy9P9erV0+DBg/Xhhx/aHQdAMfnxxx8LDtfs3LlTNWrU0IgRIxQbG6uoqCgO1wDFjEIJv/fMM8/o448/VmpqqsLCwuyOA+AmnThxQpMnT5Zpmlq3bp3Kli2rwYMHyzAM9erVS4GBgXZHBHwWhRJ+LyUlRU2aNFFcXJwMw7A7DoAbkJmZqVmzZsk0TS1YsECWZalPnz4yDEODBg1S2bJl7Y4I+AUKJSCpW7ducjqdWrZsmd1RAFxDXl6eli5dKtM0lZCQoIyMDHXo0EGGYWj48OGqXr263REBv0OhBCR9/fXXeuCBB7R7925FRkbaHQdAIZZlafPmzQWHa9LS0tS0adOCwzX8vgXsRaEE9L9ls/DwcP32t7/Vyy+/bHccAD/ZvXu3TNPUhAkTlJycrFq1amnUqFEyDEN33HEHh2sAD0GhBH7y61//WrNmzdL+/fvZvA/Y6NixY5o0aZJM09TGjRtVvnx5DRkyRIZhqEePHgoICLA7IoBCKJTATzZv3qyoqCjNmTNH/fv3tzsO4FcyMjI0Y8YMmaapxYsXy+l0qm/fvjIMQwMHDmQCA+DhKJTATyzLUuvWrRUZGanp06fbHQfwebm5uVq8eLFM09SMGTOUmZmpzp07yzAMDRs2TFWrVrU7IoDrRKEELvHBBx/o97//vQ4dOsRt2IASYFmWNm7cqLi4OE2ePFnHjx9X8+bNFRsbq1GjRqlBgwZ2RwRwEyiUwCVOnTql2rVr6+WXX9bTTz9tdxzAZyQlJRUcrtmzZ48iIiIKDte0atWKwzWAl6NQAoWMGjVKW7du1Y4dO/hLDnDD0aNHNXHiRMXFxWnLli2qUKGChg0bJsMw1LVrVw7XAD6EQgkUsmTJEt19991au3atOnbsaHccwKukp6crISFBpmlq6dKlCgwMVP/+/WUYhvr376/Q0FC7IwIoARRKoJD8/HxFRkaqe/fu+vzzz+2OA3i8nJwcLVy4UHFxcZo1a5YuXLigbt26yTAMDR06VJUrV7Y7IoASRqEEivCPf/xDb775plJTU1W+fHm74wAeJz8/X+vWrZNpmpo8ebJOnTql22+/XYZhaNSoUapbt67dEQGUIgolUIQDBw6oQYMG+vTTT/Xwww/bHQfwGDt27JBpmjJNU/v371fdunU1evRoGYahli1b2h0PgE0olMAV9O3bV2fOnNH69evtjgLY6vDhw4qPj5dpmtq6dasqV65ccLimc+fOcjqddkcEYDMKJXAFU6dO1bBhw/TDDz+oefPmdscBStXZs2c1bdo0xcXFacWKFQoODtbAgQMVGxure+65RyEhIXZHBOBBKJTAFeTk5CgiIkIPPPCA3n77bbvjACUuOztb8+bNk2mamjNnjnJyctSjRw8ZhqEhQ4aoYsWKdkcE4KEolMBV/P73v9fXX3+tw4cPKzg42O44QLHLz8/X6tWrZZqmpkyZojNnzqhNmzYyDEMjR45URESE3REBeAEKJXAVP/zwg1q0aKEpU6YoJibG7jhAsdm2bZtM01R8fLwOHjyoBg0ayDAMGYahW2+91e54ALwMhRK4hvbt26ty5cqaP3++3VEAtxw4cEDx8fGKi4vT999/r6pVq2r48OGKjY1Vhw4duDMUgJtGoQSuYfz48XrkkUcKRqQA3uT06dOaMmWKTNPUqlWrFBYWpkGDBskwDPXu3ZutHACKBYUSuIZz584pPDxcf/7zn/Xcc8/ZHQe4pgsXLmjOnDkyTVNz586Vy+VSr169ZBiGBg8ezLB+AMWOQglch4ceekjLly/Xnj17mLkHj+RyubRixQqZpqlp06YpPT1dUVFRMgxDI0aMUK1ateyOCMCHUSiB67B27Vp17txZS5YsUc+ePe2OA0iSLMvS1q1bCw7XHDlyRJGRkQWHa5o0aWJ3RAB+gkIJXAfLsnTrrbeqTZs2io+PtzsO/NyPP/6oCRMmyDRN7dy5U9WrV9fIkSNlGIbatWvH4RoApS7Q7gCAN3A4HBozZoyee+45nTp1SlWqVLE7EvzMiRMnCg7XrF27VmXKlNHgwYP19ttvq1evXgoKCrI7IgA/xhVK4DqlpaWpTp06euedd/Tb3/7W7jjwA5mZmZo1a5ZM09SCBQtkWZZ69+6t2NhYDRo0SGXLlrU7IgBIolACN2TIkCHau3evvv32W5YVUSLy8vK0bNkymaap6dOnKyMjQ+3bt5dhGBo+fLhq1Khhd0QAuAyFErgBc+fO1YABA7R582bdeeeddseBj7AsS5s3b5Zpmpo4caLS0tLUtGlTGYah0aNHKzIy0u6IAHBVFErgBuTl5al+/foaNGiQPvroI7vjwMvt2bNHpmnKNE0lJyerVq1aBYdr7rzzTq6CA/AaFErgBv3tb3/Thx9+qCNHjqhMmTJ2x4GXOXbsmCZNmiTTNLVx40aVK1dOQ4YMUWxsrLp3767AQM5KAvA+FErgBu3Zs0eNGjXSV199pfvvv9/uOPAC58+f14wZM2SaphYtWiSHw6G+ffvKMAwNHDiQf5gA8HoUSuAmdO/eXZZlacWKFXZHgYfKzc3V4sWLZZqmZsyYoczMTHXq1EmxsbEaNmyYqlatandEACg2FErgJsTFxen+++9XSkqKGjVqZHcceAjLsrRx40aZpqlJkybp+PHjat68ecHhmgYNGtgdEQBKBIUSuAlZWVkKDw/Xb37zG7366qt2x4HNkpKSZJqmJkyYoD179qh27doaPXq0DMNQq1atOFwDwOdRKIGb9NhjjykhIUEHDhzgIIUfOnr0qCZOnCjTNLV582ZVqFBBMTExMgxDd911lwICAuyOCAClhkIJ3KRvvvlGd955p2bPnq0BAwbYHQel4Ny5c5o+fbpM09TSpUsVGBiofv36yTAMDRgwQKGhoXZHBABbUCgBN7Rp00YNGjRQQkKC3VFQQnJycrRw4UKZpqlZs2YpKytLd911lwzDUExMjCpXrmx3RACwHYUScMO///1vPfnkkzp06JBq1apldxwUE8uytG7dOsXFxWny5Mk6deqUWrZsqdjYWI0aNUp169a1OyIAeBQKJeCG06dPKzw8XP/4xz/0pz/9ye44cNOOHTsKDtfs27dPdevWLThc07JlS7vjAYDHolACbho9erS2bNmiXbt2cZrXCx0+fFjx8fEyTVNbt25VpUqVNGzYMBmGoS5dusjpdNodEQA8HoUScNOyZcvUs2dPrV69Wp07d7Y7Dq7D2bNnNW3aNJmmqeXLlys4OFgDBw6UYRjq27evQkJC7I4IAF6FQgm4KT8/X40aNdJdd92l//73v3bHwRVkZ2dr/vz5Mk1Ts2fPVk5Ojrp37y7DMDR06FBVrFjR7ogA4LUolEAxePnll/Xaa68pNTVVFSpUsDsOfpKfn6/Vq1fLNE1NmTJFZ86cUZs2bWQYhkaOHKmIiAi7IwKAT6BQAsXg0KFDql+/vsaNG6exY8faHcfvbd++XXFxcYqPj9fBgwfVoEGDgsM1zZs3tzseAPgcCiVQTPr166eTJ09q48aNdkfxSwcPHtSECRNkmqa2b9+uKlWqaMSIETIMQx07duTAFACUIAolUEymTZummJgYbd++XS1atLA7jl84ffq0pk6dKtM0tXLlSoWGhmrQoEEyDEN9+vRRcHCw3REBwC9QKIFikpOTozp16sgwDL377rt2x/FZFy5c0Jw5c2SapubNm6e8vDz16tVLhmFo8ODBKl++vN0RAcDvUCiBYvT000/riy++0OHDhxk9U4xcLpdWrlwp0zQ1depUpaenq23btgWHa7hLEQDYi0IJFKOdO3eqefPmmjx5soYNG2Z3HK9mWZa2bt0q0zQVHx+vI0eOqGHDhoqNjdXo0aPVtGlTuyMCAH5CoQSKWceOHVWhQgUtWLDA7ihead++fQWHa3bs2KHq1asXHK6Jjo7mcA0AeCAKJVDMPvvsM40dO1b79u1TvXr17I7jFU6ePKnJkyfLNE2tXbtWZcqU0eDBg2UYhnr16qWgoCC7IwIAroJCCRSzc+fOKTw8XH/84x/1wgsv2B3HY2VmZmr27NkyTVPz58+XZVnq3bu3DMPQoEGDVK5cObsjAgCuE4USKAFjxozR0qVLtXfvXjmdTrvjeIy8vDwtW7ZMpmlq+vTpysjIUHR0tAzD0IgRI1SjRg27IwIAbgKFEigB69atU6dOnbRo0SLdfffddsexlWVZ2rJli0zT1MSJE3X06FE1adJEhmFo9OjRatSokd0RAQBuolACJcCyLN122226/fbbNXHiRLvj2GLPnj0yTVOmaSo5OVk1a9bUyJEjFRsbqzvvvJPDNQDgQwLtDgD4IofDoTFjxuivf/2rTp48qapVq9odqVQcP35ckyZNkmma2rBhg8qVK6chQ4bogw8+UI8ePRQYyB85AOCLuEIJlJBjx44pIiJCb7/9tn73u9/ZHafEnD9/XjNmzJBpmlq0aJEcDofuueceGYahe++9V2XKlLE7IgCghFEogRI0dOhQpaSk6LvvvvOpJd68vDwtXrxYpmkqISFBmZmZ6tSpkwzD0LBhw1StWjW7IwIAShGFEihB8+bNU//+/bVp0yZFRUXZHcctlmVp06ZNiouL06RJk3T8+HHdeuutBYdrbrnlFrsjAgBsQqEESpDL5VL9+vU1YMAAjRs3zu44NyU5ObngcM2ePXtUu3ZtjRo1SoZhqHXr1j515RUAcHMolEAJe/bZZ/XBBx8oNTXVa/YTHj16VBMnTpRpmtq8ebMqVKigoUOHyjAMdevWTQEBAXZHBAB4EAolUML27t2ryMhIffnll3rggQfsjnNF586dU0JCgkzT1JIlSxQQEKD+/fvLMAz1799fYWFhdkcEAHgoCiVQCnr27Km8vDytXLlSZ7Ny9cORszp1PkcOh0OVywTpttoVVTGs9O9XnZubq4ULFyouLk6zZs1SVlaWunbtKsMwFBMToypVqpR6JgCA96FQAqVg3Jfx+st/Zqlp3weVlpFX5GPqVA7TsDvralRUXdWoEFpiWSzL0rp162SapiZPnqyTJ0+qZcuWMgxDo0aNUr169UrsvQEAvolCCZSgC7kuvbM4WePX7JXL5ZLDefW9h86fzreM7dJQT/VqotCg4turuGPHDpmmqQkTJmjfvn2qU6eORo8eLcMwdPvttxfb+wAA/A+FEighyWnnNParzTpwOlM3+rvM4ZDqVymj/9zfVo1rlr/pDEeOHFF8fLxM09S3336rSpUqadiwYTIMQ126dJHT6bzp1wYA4CIKJVACdqSma8Qn65WZ45LrJn+LBTgdKhscoEmPdNCt4RWu+3lnz57V9OnTFRcXp+XLlys4OFgDBgyQYRjq16+fQkJCbioPAABXQqEEitmJjGzd/e5KpWflyuXm764Ah1QxLFiLn+qqquWuXASzs7M1f/58maap2bNnKycnR926dVNsbKyGDBmiSpUquRcEAICroFACxezRuC1avCPtilcmrbxcnVkdp/M/LFf+hQwFVW+gSl3vV9gtbYp8fIDDoXta1NKHo+/42dfz8/O1evVqmaapqVOn6vTp02rdurUMw9DIkSNVp06dYv9sAAAUhUIJFKPlScf0yy8Sr/qY4zPfVGbSWlVoO0iBVWrr/PYlyk5NUc1Rryq07m1XfN5Xv2ynrk2qa/v27QWHaw4ePKj69evLMAwZhqHmzZsX90cCAOCaKJRAMbr/s41at+fkFa9OZh9J0tGv/qBK3R9SxeghkiQrL0dHxj+mgLIVVev+t4p8ntMh1Qk4pzMzX9X27dtVpUoVDR8+XIZhqGPHjhyuAQDYKtDuAICvOHg6U6t3n7jqYzKT1koOp8q3vqfga47AYJVrdbfOrPxKeenHFVih+mXPy7ek/bnl1KZFW73yyivq06ePgoODi/0zAABwMyiUQDHZ9OOpaz4mJ22vgqpEyBny83t6B4c3Kfh+UYVSkhwOhx7840sa2CbC/bAAABQj1smAYrL90FkFXpxMfgWujFMKKFf5sq8HlKtS8P0rCXQ6tP3wWfdCAgBQAiiUQDE5cDpTeflX35Js5eVIAZffs9sRGPz/37+CvHxL+09luhcSAIASQKEEikmuK/+aj3EEBkuu3Mu+frFIXiyW7rwHAACljUIJFJOwoABdfcH7f0vbrozTl3394lL3xaXvojgcUpng4ru3NwAAxYVCCRSTxjXKKeAaeyiDazRU7qnDys/++dJ1zpHk/32/ZsMrPtfpcKhxjZu/rzcAACWFQgkUk5Z1Kl1zD2WZZp0kK1/nti4o+JqVl6uM7YsVXLvpFU94S5Ir31LLiIrFlhcAgOLC2CCgmHRoWFXBAU7lXGWfY0jtpirTrLPOrPxS+ZlnFFi5ts5vX6q8s8dUs+8TV339kECn2t1y5SVxAADswhVKoJhUDAvSfa1rX3PZu9qA36tC20E6//1ynVr8iaz8PNWIeV6h9Vpc8TkBTocGt4lQxbDLT4gDAGA3br0IFKOko+fU9/1VusbK9w0LcDq04Hdd1LgmeygBAJ6HK5RAMWpaq7we7974mqe9b4RD0hM9GlMmAQAei0IJFLPHuzfS7XUqXnPp+3oEOBxqXbeSft0tshiSAQBQMiiUQDELDnTqq4eiVSvEJSvfddOv43RIt4aX1xe/bKegAH6rAgA8F39LASVgf8pObXv3l6p+fp+k/w0lv14XL2wOaVNHEx/pwEEcAIDH41AOUMxOnDihqKgoVapUSWvWrNHGgxl6ee5O7T1xXgFOh1xXOLFz8XuR1cvq2X7N1b1ZjVJODgDAzaFQAsUoNzdXffr00fbt27V582bVr19fkmRZljbtO6WEbw9ry/7T2nM8o+AkeIDDocgaZXVnvcoa3KaOohpUluNGLmkCAGAzBpsDxejpp5/W6tWrtWTJkoIyKUkOh0PRt1RV9C1VJUnZeS5lXMiTw+FQ2ZAAhQRyj24AgPeiUALF5PPPP9f777+vjz76SHfddddVHxsSGKCQcpRIAIBvYMkbKAbr169Xt27d9OCDD2rcuHEsWQMA/AqFEnDT4cOH1bZtW0VGRmrZsmUKDg62OxIAAKWKQgm44cKFC+ratauOHj2qxMRE1axZ0+5IAACUOvZQAjfJsiw98sgj2r59u9auXUuZBAD4LQolcJPeffddff3115owYYLuuOMOu+MAAGAblryBm7Bo0SL17dtXf/zjH/X666/bHQcAAFtRKIEbtHv3bkVFRalDhw6aPXu2AgIY/wMA8G8USuAGpKenq3379nK5XNq4caMqVapkdyQAAGzHHkrgOuXn5+v+++/X4cOHKZMAAFyCQglcp7///e+aPXu2Zs+erWbNmtkdBwAAj0GhBK7D1KlT9dJLL+m1115T//797Y4DAIBHYQ8lcA3btm1Thw4dNHDgQMXHx3NbRQAACqFQAldx4sQJRUVFqXLlylqzZo3KlCljdyQAADwOS97AFeTm5mr48OE6f/68Vq5cSZkEAOAKKJTAFfzhD3/Q6tWrtXTpUtWrV8/uOAAAeCwKJVCEzz77TB988IE+/vhjde3a1e44AAB4NPZQAoWsW7dO3bp100MPPaRx48bZHQcAAI9HoQQucejQIbVt21aNGzfW0qVLFRwcbHckAAA8HoUS+ElWVpa6du2qtLQ0JSYmqmbNmnZHAgDAK7CHEpBkWZYeeeQR/fDDD1qzZg1lEgCAG0ChBCS9++67iouLU3x8vO644w674wAA4FVY8obfW7hwofr166c//elPeu211+yOAwCA16FQwq+lpKSoXbt26tixo2bNmqWAgAC7IwEA4HUolPBb6enpat++vfLz87Vx40ZVrFjR7kgAAHgl9lDCL+Xn5ys2NlaHDx/Wpk2bKJMAALiBQgm/9MILL2jOnDmaM2eOmjZtanccAAC8GoUSfmfKlCl6+eWX9frrr6tfv352xwEAwOuxhxJ+5bvvvlPHjh117733asKECXI4HHZHAgDA61Eo4TdOnDihtm3bqkqVKlqzZo3KlCljdyQAAHwCS97wC7m5uRo2bJgyMzO1atUqyiQAAMWIQgm/8Pvf/15r1qzRsmXLVK9ePbvjAADgUyiU8Hnjx4/Xv//9b40bN05dunSxOw4AAD6HPZTwaevWrVO3bt00ZswYffzxx3bHAQDAJ1Eo4bMOHTqktm3bqkmTJlqyZImCg4PtjgQAgE+iUMInZWVlqWvXrkpLS9PmzZtVo0YNuyMBAOCz2EMJn2NZlh555BH98MMPWrt2LWUSAIASRqGEz3nnnXcUFxeniRMnqk2bNnbHAQDA57HkDZ+ycOFC9evXT3/+85/16quv2h0HAAC/QKGEz0hJSVG7du3UqVMnzZw5UwEBAXZHAgDAL1Ao4RPS09PVvn175efna+PGjapYsaLdkQAA8BvsoYTXy8/Pl2EYOnLkCGUSAAAbUCjh9Z5//nnNnTtXc+fOVdOmTe2OAwCA36FQwqtNnjxZr7zyit544w317dvX7jgAAPgl9lDCa23dulWdOnXSoEGDZJqmHA6H3ZEAAPBLFEp4pePHjysqKkpVq1bV6tWrVaZMGbsjAQDgt5x2BwBuVG5uroYNG6asrCwlJCRQJgEAsBl7KOF1nnrqKa1bt07Lli1TvXr17I4DAIDfo1DCq/znP//Rhx9+qE8++USdO3e2Ow4AABB7KOFF1q5dq+7du+vhhx/WRx99ZHccAADwEwolvMLBgwcVFRWlpk2bavHixQoODrY7EgAA+AmFEh4vKytLXbp00fHjx5WYmKgaNWrYHQkAAFyCPZTwaJZlaezYsdqxY4fWrl1LmQQAwANRKOHR3n77bZmmqYkTJ6pNmzZ2xwEAAEVgyRsea8GCBerfv7/+8pe/6JVXXrE7DgAAuAIKJTxScnKy2rVrpy5dumjmzJlyOpnBDwCAp6JQwuOkp6crOjpakrRhwwZVrFjR5kQAAOBq2EMJj5Kfny/DMJSamqpNmzZRJgEA8AIUSniU5557TvPmzdPcuXPVpEkTu+MAAIDrQKGEx5g0aZJeffVVvfnmm7rnnnvsjgMAAK4TeyjhEbZu3aqOHTtq8ODBiouLk8PhsDsSAAC4ThRK2O748eNq27atqlWrpjVr1igsLMzuSAAA4AYwiwW2ys3NVUxMjC5cuKAZM2ZQJgEA8ELsoYStnnzySa1fv17Lli1T3bp17Y4DAABuAoUStvn000/10Ucf6dNPP1Xnzp3tjgMAAG4SeyhhizVr1qhHjx4aO3asPvzwQ7vjAAAAN1AoUeoOHjyotm3bqlmzZlqyZImCgoLsjgQAANxAoUSpyszMVJcuXXTixAlt3rxZ1atXtzsSAABwE3soUWosy9LYsWO1c+dOrVu3jjIJAICPoFCi1Lz11luaMGGCJk2apNatW9sdBwAAFBOWvFEqFixYoH79+umZZ57RK6+8YnccAABQjCiUKHHJyclq166dunbtqhkzZsjpZJ4+AAC+hEKJEnX27Fm1b99eDodDGzZsUIUKFeyOBAAAihl7KFFiXC6XDMPQ0aNHtWnTJsokAAA+ikKJEvP8889r/vz5mjdvnho3bmx3HAAAUEIolCgRkyZN0quvvqp//vOf6tOnj91xAABACWIPJYrd1q1b1bFjRw0ZMkRff/21HA6H3ZEAAEAJolCiWB07dkxRUVGqXr26Vq9erbCwMLsjAQCAEsb8FhSbnJwcxcTEKDs7WzNmzKBMAgDgJ9hDiWLz5JNPasOGDVq+fLnq1KljdxwAAFBKKJQoFp988ok+/vhjffrpp+rUqZPdcQAAQCliDyXctnr1avXo0UO/+tWv9O9//9vuOAAAoJRRKOGWAwcOqG3btmrevLkWL16soKAguyMBAIBSRqHETcvMzFSXLl108uRJJSYmqnr16nZHAgAANmAPJW6KZVl6+OGHtWvXLq1du5YyCQCAH6NQ4qb885//VHx8vCZPnqzWrVvbHQcAANiIJW/csHnz5mnAgAH661//qpdfftnuOAAAwGYUStyQpKQkRUdHq2vXrpoxY4acTmbjAwDg7yiUuG5nz55VdHS0nE6nNmzYoAoVKtgdCQAAeAD2UOK6uFwuGYahtLQ0bdq0iTIJAAAKUChxXZ577jnNnz9f8+bNU+PGje2OAwAAPAiFEtc0adIkvfbaa3rrrbfUp08fu+MAAAAPwx5KXNW3336rTp06aejQofrqq6/kcDjsjgQAADwMhRJXdOzYMUVFRalGjRpatWqVwsLC7I4EAAA8EDNfUKScnBzFxMQoOztbCQkJlEkAAHBF7KFEkZ544glt2LBBK1asUJ06deyOAwAAPBiFEpcZN26cxo0bp/Hjx6tjx452xwEAAB6OPZT4mdWrV6tHjx569NFH9cEHH9gdBwAAeAEKJQocOHBAbdu21W233aZFixYpKCjI7kgAAMALUCghScrMzFTnzp116tQpbd68WdWqVbM7EgAA8BLsoYQsy9KYMWOUlJSkdevWUSYBAMANoVBCb775piZOnKjJkyerVatWdscBAABehiVvPzdv3jwNGDBAf/vb3/TSSy/ZHQcAAHghCqUfS0pKUrt27dStWzclJCTI6WTOPQAAuHEUSj915swZRUdHKzAwUOvXr1eFChXsjgQAALwUeyj9kMvlkmEYOnbsmBITEymTAADALRRKP/Tss89qwYIFmj9/vho1amR3HAAA4OUolH4mPj5er7/+ut5++2317t3b7jgAAMAHsIfSj3zzzTfq3LmzYmJi9OWXX8rhcNgdCQAA+AAKpZ84duyY2rZtq1q1amnlypUKCwuzOxIAAPARzInxAzk5OYqJiVFubq4SEhIokwAAoFixh9IPPPHEE9q4caNWrFihiIgIu+MAAAAfQ6H0cePGjdO4ceP02WefqUOHDnbHAQAAPog9lD5s1apV6tmzp37961/r/ffftzsOAADwURRKH7V//35FRUWpRYsWWrhwoYKCguyOBAAAfBSF0gdlZmaqU6dOOnPmjBITE1WtWjW7IwEAAB/GHkofY1mWHnroISUnJ2v9+vWUSQAAUOIolD7mjTfe0KRJkzR16lTdfvvtdscBAAB+gCVvHzJ37lwNHDhQzz77rP7xj3/YHQcAAPgJCqWP2LVrl6Kjo9WtWzclJCTI6WRmPQAAKB0USh9w5swZRUdHKzAwUOvXr1eFChXsjgQAAPwIeyi9nMvl0ujRo3X8+HElJiZSJgEAQKmjUHq5v/3tb1q4cKEWLFigyMhIu+MAAAA/RKH0YvHx8XrjjTf0zjvv6O6777Y7DgAA8FPsofRSW7ZsUefOnTV8+HB98cUXcjgcdkcCAAB+ikLphdLS0tS2bVuFh4dr1apVCg0NtTsSAADwY8yW8TI5OTmKiYlRXl6eEhISKJMAAMB27KH0Mr/73e+0adMmrVixQhEREXbHAQAAoFB6k3HjxumTTz7R559/rg4dOtgdBwAAQBJ7KL3GqlWr1LNnT/3mN7/Rv/71L7vjAAAAFKBQeoH9+/crKipKLVu21IIFCxQUFGR3JAAAgAIUSg93/vx5de7cWWfPnlViYqKqVq1qdyQAAICfYQ+lB7MsSw899JBSUlK0fv16yiQAAPBIFEoP9vrrr2vy5MmaOnWqWrZsaXccAACAIrHk7aHmzJmje++9V88995xefPFFu+MAAABcEYXSA+3cuVPR0dHq0aOHpk+fLqeT+fMAAMBzUSg9zJkzZ9SuXTsFBwdr/fr1Kl++vN2RAAAAroo9lB7E5XJp1KhROnHihBITEymTAADAK1AoPchf//pXLVq0SAsXLlRkZKTdcQAAAK4LhdJDTJgwQW+++abeffdd9erVy+44AAAA1409lB5gy5Yt6ty5s0aMGKH//ve/cjgcdkcCAAC4bhRKm6Wlpalt27aqXbu2Vq5cqdDQULsjAQAA3BDm0dgoJydHQ4cOlcvlUkJCAmUSAAB4JfZQ2sSyLD3++ONKTEzUypUrVbt2bbsjAQAA3BQKpU3GjRun//znP/r888/Vvn17u+MAAADcNPZQ2mDlypXq1auXHnvsMb333nt2xwEAAHALhbKU7d+/X23bttXtt9+uhQsXKjCQi8QAAMC7UShL0fnz59W5c2edPXtWiYmJqlq1qt2RAAAA3MblsVJiWZYeeughpaSkaP369ZRJAADgMyiUpeT111/X5MmTNW3aNLVs2dLuOAAAAMWGOZSlYPbs2frb3/6mF154QUOGDLE7DgAAQLFiD2UJ27lzp6Kjo9WzZ09NmzZNTicdHgAA+BYKZQk6ffq0oqOjFRwcrPXr16t8+fJ2RwIAACh27KEsIS6XS6NGjdLJkye1adMmyiQAAPBZFMoS8swzz2jJkiVauHChIiMj7Y4DAABQYiiUJcA0Tf3zn//Ue++9p549e9odBwAAoESxh7KYbd68WV26dNHIkSP1+eefy+Fw2B0JAACgRFEoi9HRo0cVFRWliIgIrVixQqGhoXZHAgAAKHHMsCkm2dnZGjp0qFwul6ZPn06ZBAAAfoM9lMXAsiw9/vjj2rx5s1atWqXatWvbHQkAAKDUUCiLwccff6zx48friy++UHR0tN1xAAAAShV7KN20YsUK3X333Xr88cf17rvv2h0HAACg1FEo3bBv3z5FRUWpVatWWrBggQIDueALAAD8D4XyJp0/f16dOnXSuXPntGnTJlWtWtXuSAAAALbgktpNsCxLv/zlL7V7925t2LCBMgkAAPwahfImvPbaa5oyZYqmT5+uFi1a2B0HAADAVsyhvEGzZ8/Ws88+q7///e8aPHiw3XEAAABsxx7KG7Bz505FR0erV69emjp1qpxO+jgAAIDfFspcV75SjmVoz/EMZefmKzjQqVuqlVXTmuUVHHh5UTx9+rTatWun0NBQrVu3TuXLl7chNQAAgOfxqz2UrnxLK5KO6av1+7Vu7wnlui7v0gFOh9rWr6xfdGigu5vXVFCAU3l5eRo5cqROnTqlxMREyiQAAMAl/KZQfnPgtH4/eav2ncxUgMMh1xUuzLryLW3ed0obfzyl8IqheiumlWZ88oaWLl2qhQsXqmHDhqWcHAAAwLP5/JK3ZVl6Z3Gy/r18txwOKf8GPq3zp8enb56l5wfcpief+F3JBQUAAPBSPn2F0rIs/W3Gdk3YdPCn/76x518snxXuHKiUauFy5VsKcDqKOSUAAIB38+ljyuNW7S0ok25xODTv+6N6c+Eu918LAADAx/jsknfS0XPq98Fqua6wxp1zfL/OrpmgnKO75Tp/Ro6gEAVVrasK0UNUpnF0kc9xSJr6aAfdWb9KCSYHAADwLj57hfKZhG1X/b4r/Zjyc7JUtmVPVe41VhU7jpAkHZ/2ks5tXVDkcxwO6Y9Tt8lHOzgAAMBN8ckrlD8cOav+H6y54edZ+S6lfvGkrLxcRTwy7oqPm/BwtDpGVnMnIgAAgM/wySuU8ZsO3NThGYczQIHlqyk/O+OKjwlwOhS3Yb878QAAAHyKT57yXrP7xBX3ThaWn3NBVl628rMzlZWyUVl7t6jMrV2u+HhXvqX1e08WV1QAAACv53OF8nx2nvafyrzux59eNl4ZF/dMOpwq06SDqvT+9dWfk5mrtPQLqlkh1J2oAAAAPsHnCmXq2awbmjdZIWqQyjTrLNe5k8rctUaWlS+5cq/5vIOnMimUAAAA8sE9lEXdn/tqgqrWVViD1irXsqdqDHtBVs4FHZv6j2ue5M5x5bsTEwAAwGf4XKEsExzg3vObdVJOaoryTh2+xvv43MVdAACAm+JzhTKiUpiCA27+Y1m52ZKk/OzzV3yMQ1KjGuVu+j0AAAB8ic8VysAAp24NL3/Nx7nOn7nsa5YrT+e/XyZHYIiCqtW74nPrVimjciFcoQQAAJB88FCOJPW+rZa2Hz6rq00OOrng37JyMhVSt4UCyleVK+O0zu9YobyTh1S5xxg5g8OKfF6Aw6HezWuWUHIAAADv45N3yjmRka3o15ZedRbl+R0rlbFtsXKO71N+1jk5g8MUXKuRyt858Ir38r5oxR+6qUG1ssUdGwAAwCv55BXKauVCNPzOOpq0+eAVr1KWbX6Xyja/64ZeN8D5v6uTlEkAAID/53N7KC96pt+tqlo2RDdxB8YiOSSVDQ7QP+5tUTwvCAAA4CN8tlBWCA3Sv0a2lsPhUDF1Sv0zppWqlw8pplcDAADwDT5bKCWpY2Q1fTj6Djmdjpu+Uul0SA6H9GbM7epzW63iDQgAAOADfPJQTmGJ+07piUnf6ujZC1c9+V2Y0yFVKRust4e11l1NqpdcQAAAAC/mF4VSkjJz8vTekhR9vWG/snJdcjpUZLl0OCRZUlCAU8Pb1tEf+zRTxbCgUs8LAADgLfymUF6UkZ2nmVsPa1XKcW09cEZp57ILvle1bLDa1KukTpHVNOSOOhRJAACA6+B3hbKwC7kuZeflKzjAqTA37wMOAADgj/y+UAIAAMA9Pn3KGwAAACWPQgkAAAC3UCgBAADgFgolAAAA3EKhBAAAgFsolAAAAHALhRIAAABuoVACAADALRRKAAAAuIVCCQAAALdQKAEAAOAWCiUAAADcQqEEAACAWyiUAAAAcAuFEgAAAG6hUAIAAMAtFEoAAAC4hUIJAAAAt1AoAQAA4BYKJQAAANxCoQQAAIBbKJQAAABwC4USAAAAbqFQAgAAwC0USgAAALiFQgkAAAC3UCgBAADgFgolAAAA3EKhBAAAgFsolAAAAHALhRIAAABuoVACAADALRRKAAAAuIVCCQAAALdQKAEAAOAWCiUAAADcQqEEAACAW/4PWxMT5yl6sagAAAAASUVORK5CYII=", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "G1=nx.Graph()\n", "G1.add_edge(0,1); G1.add_edge(0,3); G1.add_edge(1,2); G1.add_edge(2,0)\n", "print(\"Matrice d'adjacence du graphe G1: \\n\", adjacencyMatrix(G1))\n", "drawGraph(G1)" ] }, { "cell_type": "markdown", "id": "48036dd4", "metadata": {}, "source": [ "2. Un deuxième exemple de graphe généré aléatoirement sur le modèle Erdös-Rényi :\n", "\n", "Rappel : Le graphe aléatoire $G_{n,p}$ construit sur le modèle Erdos-Rényi est un graphe à $n$ sommets dans lequel il existe une arête entre chaque paire de sommets avec une probabilité $p$.\n", "\n", "Dans l'exemple suivant : $n=20$ et $p=\\frac15$.\n", "\n" ] }, { "cell_type": "code", "execution_count": 9, "id": "486ce256", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n=20; p=1/5\n", "oriented=False\n", "G2 = nx.generators.random_graphs.fast_gnp_random_graph(n,p,directed=oriented)\n", "drawGraph(G2,prog=\"neato\")\n" ] }, { "cell_type": "markdown", "id": "0796d25d", "metadata": {}, "source": [ "3. Un plus gros graphe : `Gcit`\n", "\n", "Il s'agit d'un graphe de citations qui contient 27770 sommets et de 352807 arcs. Chaque sommet représente un article scientifique et les arcs représentent les citations : si l'article A cite l'article B, alors il y aura un arc de A vers B." ] }, { "cell_type": "code", "execution_count": 10, "id": "1470acae", "metadata": {}, "outputs": [], "source": [ "file_name=\"cit-HepTh.txt\"\n", "Gcit = nx.DiGraph()\n", "with open(file_name, 'r') as data:\n", " for line in data:\n", " p = line.split(\" \") \n", " Gcit.add_edge(int(p[0]),int(p[1]))\n", "Gcit,mappingGcit = relabelGraph(Gcit) " ] }, { "cell_type": "markdown", "id": "f4317f31", "metadata": {}, "source": [ "# Exercice 1\n", "\n", "Écrire une fonction `powerIteration` implémentant l’algorithme de puissance itérée. Cette fonction prend en paramètre une matrice, un nombre d'itérations maximum et un réel epsilon permettant de décider de l’arrêt. Cette fonction retourne un vecteur-colonne.\n", "\n", "À chaque étape de calcul (y compris à l'étape initiale), faites en sorte que la somme des valeurs du vecteur-colonne soit égale à 1. \n", "\n", "Pour info : un vecteur-colonne peut être obtenu avec `np.ndarray(shape=(n,1))` où $n$ est la taille du vecteur." ] }, { "cell_type": "code", "execution_count": 14, "id": "5bea1d79-34e2-40f2-b5a1-74b773d27a34", "metadata": {}, "outputs": [], "source": [ "def powerIteration(A,max_iter=100,epsilon=0.0001):\n", " n = len(A)\n", " C = np.ndarray(shape=(n,1)) \n", " C.fill(1/n)\n", " for i in range(max_iter):\n", " Cprev = C\n", " C = multMatrix(A,C)\n", " C /= C.sum()\n", " delta = abs(C - Cprev)\n", " if delta.max() < epsilon:\n", " print(\"Nb itérations : \" + str(i+1))\n", " return C\n", " return C" ] }, { "cell_type": "markdown", "id": "fb173621", "metadata": {}, "source": [ "# Exercice 2 :\n", "Utilisez la fonction `powerIteration` écrite à l'exercice 1 pour calculer la centralité de vecteur propre **dans le cas non orienté** (utilisez le graphe `G1` défini plus haut). Vous fixerez un réel epsilon permettant d’indiquer la précision du calcul. Faites appel à la fonction `drawGraph` pour voir le résultat de vos calculs s’afficher sur les sommets du graphe." ] }, { "cell_type": "code", "execution_count": 15, "id": "c30b18d8-a27d-4190-a1b3-993cbad98115", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Nb itérations : 20\n", "[[0.32]\n", " [0.27]\n", " [0.27]\n", " [0.15]]\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "A = adjacencyMatrix(G1)\n", "C = powerIteration(A).round(2)\n", "print(C)\n", "drawGraph(G1,C)" ] }, { "cell_type": "markdown", "id": "de3f3431-6c44-47f9-875d-fbed464508d5", "metadata": {}, "source": [ "# Exercice 3\n", "\n", "1. Écrire une fonction `matrixPageRank` permettant de construire la matrice de passage du Page Rank qui nous permettra de calculer la centralité de vecteur propre dans le **cas orienté** . Cette fonction prend en paramètre un graphe orienté et un réel alpha correspondant au facteur de zap (dumping factor). " ] }, { "cell_type": "code", "execution_count": 19, "id": "c249e5fa", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 12. ]\n", " [ 12. ]\n", " [ 2.5]\n", " [ 5. ]\n", " [ 10. ]\n", " [ 20. ]\n", " [ 25. ]\n", " [ 50. ]\n", " [100. ]\n", " [200. ]]\n" ] } ], "source": [ "s = np.ndarray(shape=(10,1))\n", "s[1]=12\n", "print(s)" ] }, { "attachments": { "Graph_pageRank2.png": { "image/png": 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" } }, "cell_type": "markdown", "id": "5524474c", "metadata": {}, "source": [ "2. Uilisez la fonction `matrixPageRank` pour calculer la matrice de passage du graphe suivant (que vous devez construire auparavant), puis calculez la valeur du Page Rank de chaque sommet à l'aide de la fonction `powerIteration`. \n", "\n", "![Graph_pageRank2.png](attachment:Graph_pageRank2.png)\n", "\n", "La valeur du Page Rank de chaque sommet est la suivante : \n", "\n", "`[[0.31]\n", " [0.21]\n", " [0.26]\n", " [0.21]]` " ] }, { "cell_type": "code", "execution_count": null, "id": "b0074aca", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "227af138", "metadata": {}, "source": [ "3. Testez votre fonction sur le graphe de citations scientifiques `GCit`. Quel noeud est le plus important ?" ] }, { "cell_type": "code", "execution_count": null, "id": "be0ccc92", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "1c249a13", "metadata": {}, "source": [ "## Exercice 4\n", "\n", "Tentez d'accélérer le calcul de la matrice de passage pour accélérer le calcul du Page Rank. Pour se faire, il est possible de minimiser le nombre de multiplication de matrices (opérations qui sont très couteuses en temps de calcul) pour construire la matrice de passage." ] }, { "cell_type": "code", "execution_count": null, "id": "9cb87f12", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "celltoolbar": "Aucun(e)", "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.10.12" } }, "nbformat": 4, "nbformat_minor": 5 }