Determining Factors Behind the PageRank Log-Log Plot

  • Yana Volkovich
  • Nelly Litvak
  • Debora Donato
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4863)


We study the relation between PageRank and other parameters of information networks such as in-degree, out-degree, and the fraction of dangling nodes. We model this relation through a stochastic equation inspired by the original definition of PageRank. Further, we use the theory of regular variation to prove that PageRank and in-degree follow power laws with the same exponent. The difference between these two power laws is in a multiplicative constant, which depends mainly on the fraction of dangling nodes, average in-degree, the power law exponent, and the damping factor. The out-degree distribution has a minor effect, which we explicitly quantify. Finally, we propose a ranking scheme which does not depend on out-degrees.


PageRank Power laws Ranking algorithms Stochastic equations Web graph Wikipedia 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Yana Volkovich
    • 1
  • Nelly Litvak
    • 1
  • Debora Donato
    • 2
  1. 1.University of Twente, P.O. Box 217, 7500 AE, EnschedeThe Netherlands
  2. 2.Yahoo! Research, Barcelona Ocata 1, 1st floor, 08003, Barcelona CatalunyaSpain

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