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Numerical Algorithms for Personalized Search in Self-organizing Information Networks by Sep Kamvar

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Chapter Three

The Second Eigenvalue of the Google Matrix

3.1 INTRODUCTION

Before attempting to accelerate the computation of PageRank, it is useful first to prove some results regarding the convergence rate of the standard PageRank algorithm.

In this chapter, we determine analytically the modulus of the second eigenvalue for the Web hyperlink matrix used by Google for computing PageRank.

This 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 ...

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