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Date

13. 9.2014 14:45:22

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Abstract

We observe that the convergence patterns of pages in the PageRank algorithm have a nonuniform distribution. Specifically, many pages converge to their true PageRank quickly, while relatively few pages take a much longer time to converge. Furthermore, we observe that these slow-converging pages are generally those pages with high PageRank.We use this observation to devise a simple algorithm to speed up the computation of PageRank, in which the PageRank of pages that have converged are not recomputed at each iteration after convergence. This algorithm, which we call Adaptive PageRank, speeds up the computation of PageRank by nearly 30%.

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Abstract

We determine analytically the modulus of the second eigenvalue for the web hyperlink matrix used by Google for computing PageRank. Specifically, we prove the following statement: "For any matrix A=(cP + (1-c)E)**T, where P is an nxn row-stochasticmatrix, E is a nonnegative nxn rank-one row-stochastic matrix, and 0<=c<=1, the second eigenvalue of A has modulus Betrag (Lambda_sub2)<=c. Furthermore, if P has at least two irreducible closed subsets, the second eigenvalue Lambda_sub2 = c." This statement has implications for the convergence rate of the standard PageRank algorithm as the web scales, for the stability of PageRank to perturbations to the link structure of the web, for the detection of Google spammers, and for the design of algorithms to speed up PageRank.

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