Characterization of Tail Dependence for In-Degree and PageRank

  • Nelly Litvak
  • Werner Scheinhardt
  • Yana Volkovich
  • Bert Zwart
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5427)


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.


Power law graphs PageRank Regular variation Multivariate extremes 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Nelly Litvak
    • 1
  • Werner Scheinhardt
    • 1
  • Yana Volkovich
    • 1
  • Bert Zwart
    • 2
  1. 1.Dept. of Applied MathematicsUniversity of TwenteEnschedeThe Netherlands
  2. 2.CWI, Science Park AmsterdamAmsterdamThe Netherlands

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