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where they find the PageRank (PR) of page A, by taking the the PageRank of all pages that link to A, defined here as T , divided by the number of outgoing links on each page, defined as L. The parameter d is a dampening factor, which can be set from between 0 and 1, given as 0.85 in their paper. It is meant to simulate the number of links that a random surfer will follow before they go to a random, unlinked page. Brin and Page (1998) also claimed that the PageRanks formed a probability distribution over all web pages, so that the sum of all of them would be 1. This is not the case with the algorithm they gave, so it must be modified as such: (1 − d) [PR(T1) PR(Tn)] PR(A)= N +d L(T1) +...+ L(Tn) , (III.2) Where N is the total number of pages in the network. With this modification it then forms a probability distribution. By performing a number of iterations of the algorithm, the PageRanks of all pages in the network can be determined. This can be written generally as: (1−d) ∑ PR(aj) PR(ai)= N +d aj ∈G(ai ) L(aj) , (III.3) (III.4) Where ai is a webpage, and aj is a page with an outgoing link to ai. As shown in Section 2.2, the link matrix can be defined by: 1/lpj Hij = 0 if pj links to pi otherwise , Where lpj is equal to the number of outgoing links on page pj . The PageRanks for the model network are shown in Figure 2.2. Giving each page a starting PageRank value of N1 , then iterating the algorithm until the dif- 11PDF Image | MATHEMATICS BEHIND GOOGLE PAGERANK ALGORITHM
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