Haveliwala, T.; Kamvar, S.: ¬The second eigenvalue of the Google matrix (2003)
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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.
