Page Ranking Algorigthm

page_rank.py

import numpy as np
import numpy.linalg as la
from readonly.PageRankFunctions import *
np.set_printoptions(suppress=True)

def pageRank(linkMatrix, d) :
    n = linkMatrix.shape[0]
    M = d * linkMatrix + (1-d)/n * np.ones([n, n]) # np.ones() is the J matrix, with ones for each entry.
    r = 100 * np.ones(n) / n # Sets up this vector (n entries of 1/n × 100 each)
    lastR = r
    r = M @ r
    i = 0
    while la.norm(lastR - r) > 0.01 :
        lastR = r
        r = M @ r
        i += 1
    
    return r
  

L = np.array([[0,   1/2, 1/3, 0, 0,   0 ],
              [1/3, 0,   0,   0, 1/2, 0 ],
              [1/3, 1/2, 0,   1, 0,   1/2 ],
              [1/3, 0,   1/3, 0, 1/2, 1/2 ],
              [0,   0,   0,   0, 0,   0 ],
              [0,   0,   1/3, 0, 0,   0 ]])


eVals, eVecs = la.eig(L) # Gets the eigenvalues and vectors
order = np.absolute(eVals).argsort()[::-1] # Orders them by their eigenvalues
eVals = eVals[order]
eVecs = eVecs[:,order]

r = eVecs[:, 0]
100 * np.real(r / np.sum(r))

%pylab notebook
r = pageRank(generate_internet(100), 0.9)
plt.bar(arange(r.shape[0]), r);