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@mikk-c
Created October 3, 2018 09:07
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{
"cells": [
{
"cell_type": "code",
"execution_count": 76,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"#The goal of the exercise is calculate the stationary distribution and to study its correlation with both pagerank and degree \n",
"import networkx as nx \n",
"import numpy as np \n",
"from scipy import stats \n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": 101,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"#Read the input data\n",
"g = nx.read_edgelist(\"../session4/data/facebook.txt\", delimiter=',')"
]
},
{
"cell_type": "code",
"execution_count": 102,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"#Let's calcualte the stationary distribution\n",
"\n",
"#1- Get the subgraph constituted of the biggest component in your graph \n",
"g = g.subgraph(max(nx.connected_components(g),key=len))\n",
"\n",
"#2- Get the adjacency matrix of your graph\n",
"adj_mat = nx.to_numpy_matrix(g)\n",
"\n",
"degree_vector = adj_mat.sum(axis=1)\n",
"\n",
"#3- Column-normalize the ajacency matrix \n",
"adj_mat = adj_mat/adj_mat.sum(axis=0)\n",
"\n",
"#4- Find the eigen values and the eigen vectors \n",
"eig_values, eig_vectors = np.linalg.eig(adj_mat)\n",
"\n",
"#5- Get the stationary distribution for each component \n",
"sorted_index = np.argsort(eig_values)[::-1]\n",
"eig_values_sorted = eig_values[sorted_index]\n",
"eig_vectors_sorted = eig_vectors[:,sorted_index]\n",
"\n",
"#6- Caluclate the stationary distribution \n",
"stationary_distribution = np.real(eig_vectors_sorted[:,0]/eig_vectors_sorted[:,0].sum())\n"
]
},
{
"cell_type": "code",
"execution_count": 103,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"#See of the stationary distribtuion and the degree are related \n",
"r, p = stats.pearsonr(degree_vector,stationary_distribution)\n",
"\n",
"#Try to normalize the degree vector, compare it with the stationary distribution (What do you realize?)\n",
"degree_vector_normalized = degree_vector/degree_vector.sum()\n"
]
},
{
"cell_type": "code",
"execution_count": 104,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[ 0.99685272] [ 1.36544534e-34]\n"
]
}
],
"source": [
"# See if the stationary distribution and the page rank are related \n",
"pagerank = nx.pagerank_scipy(g)\n",
"pagerank = np.matrix([pagerank[n] for n in g.nodes()]).T\n",
"\n",
"r, p = stats.pearsonr(pagerank,stationary_distribution)\n",
"\n",
"print(r,p)\n"
]
},
{
"cell_type": "code",
"execution_count": 106,
"metadata": {},
"outputs": [
{
"data": {
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fXx+//fbbB+3l5+fDzs4Ov/32G1xdXevc144dO2LBggXIycnBtWvXEBgYWKd5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\nP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rJWcZnzgmqld+/ePbZu3cqCBQvK7Pg5R973j8Bv375NkyZNciVuHx8f42snJyedvEvB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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x116148208>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"nx.draw_networkx(g, \n",
" node_size = [v*1000 for v in stationary_distribution],\n",
" with_labels = False)\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": "3.6.6"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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