Characterization of Tail Dependence for In-Degree and PageRank

Authors:
Nelly Litvak;Werner Scheinhardt;Yana Volkovich;Bert Zwart
Affiliations:
Dept. of Applied Mathematics, University of Twente, Enschede, The Netherlands 7500 AE;Dept. of Applied Mathematics, University of Twente, Enschede, The Netherlands 7500 AE;Dept. of Applied Mathematics, University of Twente, Enschede, The Netherlands 7500 AE;CWI, Science Park Amsterdam, Amsterdam, The Netherlands 1098 SJ
Venue:
WAW '09 Proceedings of the 6th International Workshop on Algorithms and Models for the Web-Graph
Year:
2009

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Abstract

The dependencies between power law parameters such as in-degree and PageRank, can be characterized by the so-called angular measure, a notion used in extreme value theory to describe the dependency between very large values of coordinates of a random vector. Basing on an analytical stochastic model, we argue that the angular measure for in-degree and personalized PageRank is concentrated in two points. This corresponds to the two main factors for high ranking: large in-degree and a high rank of one of the ancestors. Furthermore, we can formally establish the relative importance of these two factors.