The Second Eigenvalue of the Google Matrix

The Second Eigenvalue of the Google Matrix (2003)

by Taher H. Haveliwala , Sepandar D. Kamvar , Ar D. Kamvar

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Datum	Value	Source
TITLE	The Second Eigenvalue of the Google Matrix	user correction - Legacy Corrections
AUTHOR NAME	Taher H. Haveliwala	user correction - Legacy Corrections
AUTHOR AFFIL	Stanford University	user correction - Legacy Corrections
AUTHOR NAME	Sepandar D. Kamvar	user correction - Legacy Corrections
AUTHOR NAME	Ar D. Kamvar	user correction - Legacy Corrections
AUTHOR AFFIL	Stanford University	user correction - Legacy Corrections
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 , where P is an n n row-stochastic matrix, E is a nonnegative nn rank-one row-stochastic matrix, and 0 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.	user correction - Legacy Corrections
YEAR	2003	user correction - Legacy Corrections
CITATIONS	12 found	ParsCit 1.0