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URN: urn:nbn:de:0030-drops-10722
URL: http://drops.dagstuhl.de/opus/volltexte/2007/1072/
Boldi, Paolo ; Santini, Massimo ; Vigna, Sebastiano

A Deeper Investigation of PageRank as a Function of the Damping Factor

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Abstract

PageRank is defined as the stationary state of a Markov chain. The chain is obtained by perturbing the transition matrix induced by a web graph with a damping factor $alpha$ that spreads uniformly part of the rank. The choice of $alpha$ is eminently empirical, and in most cases the original suggestion $alpha=0.85$ by Brin and Page is still used. In this paper, we give a mathematical analysis of PageRank when $alpha$ changes. In particular, we show that, contrarily to popular belief, for real-world graphs values of $alpha$ close to $1$ do not give a more meaningful ranking. Then, we give closed-form formulae for PageRank derivatives of any order, and by proving that the $k$-th iteration of the Power Method gives exactly the PageRank value obtained using a Maclaurin polynomial of degree $k$, we show how to obtain an approximation of the derivatives. Finally, we view PageRank as a linear operator acting on the preference vector and show a tight connection between iterated computation and derivation.

BibTeX - Entry

@InProceedings{boldi_et_al:DSP:2007:1072,
  author =	{Paolo Boldi and Massimo Santini and Sebastiano Vigna},
  title =	{A Deeper Investigation of PageRank as a Function of the Damping Factor},
  booktitle =	{Web Information Retrieval and Linear Algebra Algorithms},
  year =	{2007},
  editor =	{Andreas Frommer and Michael W. Mahoney and Daniel B. Szyld},
  number =	{07071},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Internationales Begegnungs- und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2007/1072},
  annote =	{Keywords: PageRank, damping factor, Markov chains}
}

Keywords: PageRank, damping factor, Markov chains
Seminar: 07071 - Web Information Retrieval and Linear Algebra Algorithms
Issue date: 2007
Date of publication: 28.06.2007

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