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by Sepandar Kamvar, Taher Haveliwala (Stanford University)
(2003) 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 n × n row-stochastic
matrix, E is a nonnegative n×n rank-one row-stochastic matrix, and 0 c 1,
the second eigenvalue of A has modulus |2| c. Furthermore, if P has at least
two irreducible closed subsets, the second eigenvalue 2 = 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.
www.stanford.edu/~sdkamvar/papers/secondeigenvalue.pdf
Added by James Thornton on 2003-12-10
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