Probabilistic Relation between In-Degree and PageRank

Authors:
Nelly Litvak;Werner R. Scheinhardt;Yana Volkovich
Affiliations:
Dept. of Applied Mathematics, University of Twente, Enschede, The Netherlands 7500AE;Dept. of Applied Mathematics, University of Twente, Enschede, The Netherlands 7500AE;Dept. of Applied Mathematics, University of Twente, Enschede, The Netherlands 7500AE
Venue:
Algorithms and Models for the Web-Graph
Year:
2007

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Abstract

This paper presents a novel stochastic model that explains the relation between power laws of In-Degree and PageRank. PageRank is a popularity measure designed by Google to rank Web pages. We model the relation between PageRank and In-Degree through a stochastic equation, which is inspired by the original definition of PageRank. Using the theory of regular variation and Tauberian theorems, we 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 Web data.Categories and Subject DescriptorsH.3.3:[Information Storage and Retrieval]: Information Search and Retrieval--- Retrieval models; G.3:[Mathematics of Computing]: Probability and statistics --- Stochastic processes, Distribution functions