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2007 In-Degree and PageRank: Why Do They Follow Similar Power Laws?
N. Litvak, W. R. W. Scheinhardt, Y. Volkovich
Internet Math. 4(2-3): 175-198 (2007).

Abstract

PageRank is a popularity measure designed by Google to rank Web pages. Experiments confirm that PageRank values obey a power law with the same exponent as In-Degree values. This paper presents a novel mathematical model that explains this phenomenon. The relation between PageRank and In-Degree is modeled through a stochastic equation, which is inspired by the original definition of PageRank, and is analogous to the well-known distributional identity for the busy period in the $M/G/1$ queue. Further, we employ the theory of regular variation and Tauberian theorems to prove analytically that the tail distributions of PageRank and In-Degree differ only by a multiplicative constant, for which we derive a closed-form expression. Our analytical results are in good agreement with experimental data.

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N. Litvak. W. R. W. Scheinhardt. Y. Volkovich. "In-Degree and PageRank: Why Do They Follow Similar Power Laws?." Internet Math. 4 (2-3) 175 - 198, 2007.

Information

Published: 2007
First available in Project Euclid: 27 May 2009

zbMATH: 1206.68352
MathSciNet: MR2522875

Rights: Copyright © 2007 A K Peters, Ltd.

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Vol.4 • No. 2-3 • 2007
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