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The PageRank algorithm is applicable in web pages. Web page is a directed graph, we know that the two components of Directed graphsare -nodes and connections. The pages are nodes and hyperlinks are the connections, the connection between two nodes.

We can find out the importance of each page by the PageRank and it is accurate. The value of the PageRank is the probability will be between 0 and 1.

The PageRank value of individual node in a graph depends on the PageRank value of all the nodes which connect to it and those nodes are cyclically connected to the nodes whose ranking we want, we use converging iterative method for assigning values to PageRank.

import numpy as np import scipy as sc import pandas as pd from fractions import Fraction def display_format(my_vector, my_decimal): return np.round((my_vector).astype(np.float), decimals=my_decimal) my_dp = Fraction(1,3) Mat = np.matrix([[0,0,1], [Fraction(1,2),0,0], [Fraction(1,2),1,0]]) Ex = np.zeros((3,3)) Ex[:] = my_dp beta = 0.7 Al = beta * Mat + ((1-beta) * Ex) r = np.matrix([my_dp, my_dp, my_dp]) r = np.transpose(r) previous_r = r for i in range(1,100): r = Al * r print (display_format(r,3)) if (previous_r==r).all(): break previous_r = r print ("Final:\n", display_format(r,3)) print ("sum", np.sum(r))

[[0.333] [0.217] [0.45 ]] [[0.415] [0.217] [0.368]] [[0.358] [0.245] [0.397]] [[0.378] [0.225] [0.397]] [[0.378] [0.232] [0.39 ]] [[0.373] [0.232] [0.395]] [[0.376] [0.231] [0.393]] [[0.375] [0.232] [0.393]] [[0.375] [0.231] [0.394]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] [[0.375] [0.231] [0.393]] Final: [[0.375] [0.231] [0.393]] sum 0.9999999999999951

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