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In-Degree and PageRank: Why do they follow similar power laws?

Summary: In-Degree and PageRank:
Why do they follow similar power laws?
N. Litvak
, W.R.W. Scheinhardt and Y. Volkovich
University of Twente, Dept. of Applied Mathematics,
P.O. Box 217, 7500AE Enschede, The Netherlands;
e-mail: {n.litvak, w.r.w.scheinhardt, y.volkovich}@ewi.utwente.nl
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 bet-
ween 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 analytically prove 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.


Source: Al Hanbali, Ahmad - Department of Applied Mathematics, Universiteit Twente


Collections: Engineering