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Created November 29, 2020 22:41
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CS166 - PageRank in citation networks
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# PageRank in citation networks"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Import an Erdos-Renyi graph to use in our simulation\n",
"import networkx as nx\n",
"g = nx.erdos_renyi_graph(30, 0.05, directed=True, seed=123)\n",
"nx.draw(g, pos=nx.kamada_kawai_layout(g), with_labels=True, font_color='white')"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"{0: 0.01321914850756847,\n",
" 1: 0.04305614905051307,\n",
" 2: 0.0224184422385673,\n",
" 3: 0.020763573555365067,\n",
" 4: 0.1519409000092644,\n",
" 5: 0.015278038556628357,\n",
" 6: 0.04357199076624549,\n",
" 7: 0.08868962006965002,\n",
" 8: 0.009276594051426114,\n",
" 9: 0.027215223573378695,\n",
" 10: 0.009276594051426114,\n",
" 11: 0.009276594051426114,\n",
" 12: 0.009276594051426114,\n",
" 13: 0.021104257419853185,\n",
" 14: 0.023535500084085954,\n",
" 15: 0.009276594051426114,\n",
" 16: 0.018135203917936826,\n",
" 17: 0.009276594051426114,\n",
" 18: 0.01264966891920012,\n",
" 19: 0.05375946044542632,\n",
" 20: 0.009276594051426114,\n",
" 21: 0.011904963688854351,\n",
" 22: 0.15057445865003966,\n",
" 23: 0.02084377195458973,\n",
" 24: 0.025679331302227965,\n",
" 25: 0.02721686924658904,\n",
" 26: 0.0925438315518033,\n",
" 27: 0.009276594051426114,\n",
" 28: 0.009276594051426114,\n",
" 29: 0.03241025002937753}"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Check the graph's PageRank vector according to NetworkX (default α = 0.85)\n",
"r = nx.pagerank(g)\n",
"r"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"# Random surfer simulation of PageRank\n",
"import random as rd\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import collections\n",
"\n",
"def initialize():\n",
" global g, current_node, counter_dict, history\n",
" current_node = rd.choice(list(g.nodes))\n",
" history = [current_node]\n",
" counter_dict = {node:0 for node in g.nodes}\n",
" \n",
"def update(N, alpha = 0.85):\n",
" global g, current_node, counter_dict, history\n",
" for step in range(N):\n",
" if np.random.random() < alpha:\n",
" if len(list(g.neighbors(current_node))) == 0:\n",
" current_node = rd.choice(list(g.nodes))\n",
" else:\n",
" current_node = rd.choice(list(g.neighbors(current_node)))\n",
" else:\n",
" current_node = rd.choice(list(g.nodes))\n",
" history.append(current_node)\n",
" counts = collections.Counter(history)\n",
" for node in counts:\n",
" counts[node] *= 1/N\n",
" counter_dict[node] = counts[node]\n",
" \n",
" return counter_dict"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"{0: 0, 1: 0.05, 2: 0, 3: 0.02, 4: 0.19, 5: 0.02, 6: 0.03, 7: 0.1, 8: 0.01, 9: 0.01, 10: 0, 11: 0, 12: 0, 13: 0.01, 14: 0.03, 15: 0.02, 16: 0, 17: 0.01, 18: 0.01, 19: 0.08, 20: 0.02, 21: 0.02, 22: 0.18, 23: 0, 24: 0.04, 25: 0.01, 26: 0.12, 27: 0.01, 28: 0, 29: 0.02}\n",
"1.01\n"
]
}
],
"source": [
"initialize()\n",
"pagerank100 = update(100)\n",
"print(pagerank100)\n",
"print(sum(pagerank100.values()))"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Visualize results by varying node colors\n",
"colors = list(pagerank100[node] for node in pagerank100)\n",
"pos = nx.kamada_kawai_layout(g)\n",
"nx.draw(g, pos, node_color=colors)\n",
"node_colors = nx.draw_networkx_nodes(g, pos, nodelist=list(g.nodes), node_color=colors, \n",
" node_size=100, cmap='viridis')\n",
"plt.colorbar(node_colors)\n",
"plt.axis('off')\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Plotting values from networkx\n",
"colors = list(r.values())\n",
"pos = nx.kamada_kawai_layout(g)\n",
"nx.draw(g, pos, node_color=colors)\n",
"node_colors = nx.draw_networkx_nodes(g, pos, nodelist=list(g.nodes), node_color=colors,\n",
" node_size=100, cmap='viridis')\n",
"plt.colorbar(node_colors)\n",
"plt.axis('off')\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"# Draw plot showing average error in simulation\n",
"n_trials = 1000\n",
"n_nodes = len(g.nodes)\n",
"\n",
"Ns = np.arange(50, 1001, 10)\n",
"errors = np.empty(len(Ns))\n",
"\n",
"for i, N in enumerate(Ns):\n",
" trials = np.empty(n_trials)\n",
" for k, trial in enumerate(range(n_trials)):\n",
" initialize()\n",
" ranks = update(N)\n",
" err = np.empty(n_nodes)\n",
" for j, node in enumerate(ranks):\n",
" err[j] = abs(ranks[node] - r[node])\n",
" trials[k] = sum(err)/n_nodes\n",
" errors[i] = sum(trials)/n_trials"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(Ns, errors)\n",
"plt.xlabel('Number of steps (N)')\n",
"plt.ylabel('Average node PageRank error')\n",
"plt.show()"
]
}
],
"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": "3.7.8"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
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