Page Rank and exemple

Author: fabioamaral08

Ranking Page/PageRank/PageRank.py

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+#!/usr/bin/env python
+# coding: utf-8
+
+#Author: fabiovini08
+
+import os
+import numpy as np
+
+
+# Creates an adjacency matrix from a file
+
+#File format:   A .txt file where the first line has a number N that
+#                represents the #nodes and the following lines have numbers
+#                pairs X Y that represents the edge X -> Y
+def read_graph(filename):
+    f = open(filename,'r+')
+    lines = f.readlines()
+    f.close();
+    N = int(lines.pop(0))
+    M = np.zeros([N,N])
+    for l in lines:
+        i,j = l.split()
+        i = int(i)
+        j = int(j)
+        
+        M[i,j] = 1
+    i = 0
+    return M
+
+# absorbing node treatment 
+def dumping_fac(M,fac = 0.15):
+    A = (1-fac)*M + fac * 1/M.shape[0] * np.ones(M.shape)
+    return A
+
+# No link page treatment
+def mat_norm(M):
+    for c in (M.T):
+        s = np.sum(c)
+        if s == 0:
+            c = np.ones([1,N]) * 1/N
+        else:
+            c = 1/np.sum(c) * c
+        c.reshape([10,1])
+        M[:,i] = c;
+        i = i+1  
+    return M  
+
+#Compute the relevance of each page
+def page_rank(M, tol = 0.001, nIter = 500):
+    # Returns the vector v where each position has a value of relevance
+    # of the respective node
+
+    M = mat_norm(M)
+    M = dumping_fac(M)
+    N = M.shape[0]
+    v = np.ones([N,1]) * 1/N
+    for i in range(nIter):
+        v1 = M.dot(v)
+        err = np.linalg.norm(v-v1,2)
+        v = v1
+        if err < tol:
+            numI = i
+            break
+    return v, numI
+    
+##  Algorith Test
+
+M = read_graph('graph.txt')
+print(M)
+A = dumping_fac(M)
+print(A)
+v, it = page_rank(A)
+print(v)
+val = max(v)
+print(val, it)
+

Ranking Page/PageRank/graph.txt

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+10
+0 2
+0 4
+0 3
+2 3
+3 1
+4 2
+6 0
+8 7
+9 5
+8 9