Consider the following pages and the set of web pages that they link to: Page A

Question

Consider the following pages and the set of web pages that they link to:

Page A points to page C.

Page B points to page C.

Page C points to page D.

Consider running the PageRank algorithm on this subgraph of pages. Assume d = 0.85. Simulate the algorithm for three iterations, assuming that we start at Page A. Show the page rank scores for each page for each iteration. Order the elements in the vectors in the sequence: A, B, C, D.

use this way in your computations for this question

At t = 0 an initial probability distribution is assumed, usually PR (pi; 0) = 1/N At each time step, the computation, as detailed above, yields PR (p; t + 1) = 1 - d/N + d PR (pj; t)/L(pj),

Explanation / Answer

At t=0 PR(A) = PR(B) = PR(C) = PR(D) = 0.25

At t=1 PR(A;1) = (1-0.85)/4 = 0.0625, PR(B;1) = (1-0.85)/4 = 0.0625,

PR(C;1) = (1-0.85)/4 + 0.85*( PR(A;0)/1 + PR(B;0)/1 ) = 0.0625 + 0.85*0.5 = 0.4875

PR(D;1) = (1-0.85)/4 + 0.85*( PR(C;0)/1) = 0.0625 + 0.85*0.25 = 0.275

PR(A;2) = 0.0625, PR(B;2) = 0.0625

PR(C;2) = 0.0625 + 0.85*(PR(A;1)/1 + PR(B;1)/1) = 0.0625 + 0.85*0.125 = 0.16875

PR(D;2) = 0.0625 + 0.85*(PR(C;1)/1) = 0.0625 + 0.85*(0.4875) = 0.4768

PR(A;3) = 0.0625, PR(B;3) = 0.0625

PR(C;3) = 0.16875

PR(D;3) = 0.0625 + 0.85*(PR(C;2)/1) = 0.0625 + 0.85*(0.4768) = 0.4678

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