Determining factors behind the pagerank log-log plot

Yana Volkovich; Nelly Litvak; Debora Donato

doi:10.1007/978-3-540-77004-6_9

Determining factors behind the pagerank log-log plot

Yana Volkovich, Nelly Litvak, Debora Donato

Stochastic Operations Research

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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Abstract

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.

Original language	English
Title of host publication	Algorithms and Models for the Web-Graph
Subtitle of host publication	5th International Workshop, WAW 2007, San Diego, CA, USA, December 11-12, 2007. Proceedings
Editors	Anthony Bonato, Fan R.K. Chung
Place of Publication	Berlin, Heidelberg
Publisher	Springer
Pages	108-123
Number of pages	16
ISBN (Electronic)	978-3-540-77004-6
ISBN (Print)	978-3-540-77003-9
DOIs	https://doi.org/10.1007/978-3-540-77004-6_9
Publication status	Published - 2007
Event	5th International Workshop on Algorithms and Models for the Web-Graph, WAW 2007 - San Diego, United States Duration: 11 Dec 2007 → 12 Dec 2007 Conference number: 5

Publication series

Name	Lecture Notes in Computer Science
Publisher	Springer
Volume	4863
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Workshop

Workshop	5th International Workshop on Algorithms and Models for the Web-Graph, WAW 2007
Abbreviated title	WAW
Country	United States
City	San Diego
Period	11/12/07 → 12/12/07

Keywords

EWI-11672
MSC-60J80
METIS-245912
MSC-90B15
IR-62095
MSC-68P10

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10.1007/978-3-540-77004-6_9

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Volkovich, Y., Litvak, N., & Donato, D. (2007). Determining factors behind the pagerank log-log plot. In A. Bonato, & F. R. K. Chung (Eds.), Algorithms and Models for the Web-Graph: 5th International Workshop, WAW 2007, San Diego, CA, USA, December 11-12, 2007. Proceedings (pp. 108-123). (Lecture Notes in Computer Science; Vol. 4863). Springer. https://doi.org/10.1007/978-3-540-77004-6_9

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title = "Determining factors behind the pagerank log-log plot",

abstract = "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.",

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author = "Yana Volkovich and Nelly Litvak and Debora Donato",

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Volkovich, Y, Litvak, N & Donato, D 2007, Determining factors behind the pagerank log-log plot. in A Bonato & FRK Chung (eds), Algorithms and Models for the Web-Graph: 5th International Workshop, WAW 2007, San Diego, CA, USA, December 11-12, 2007. Proceedings. Lecture Notes in Computer Science, vol. 4863, Springer, Berlin, Heidelberg, pp. 108-123, 5th International Workshop on Algorithms and Models for the Web-Graph, WAW 2007, San Diego, United States, 11/12/07. https://doi.org/10.1007/978-3-540-77004-6_9

Determining factors behind the pagerank log-log plot. / Volkovich, Yana; Litvak, Nelly; Donato, Debora.

Algorithms and Models for the Web-Graph: 5th International Workshop, WAW 2007, San Diego, CA, USA, December 11-12, 2007. Proceedings. ed. / Anthony Bonato; Fan R.K. Chung. Berlin, Heidelberg : Springer, 2007. p. 108-123 (Lecture Notes in Computer Science; Vol. 4863).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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T1 - Determining factors behind the pagerank log-log plot

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AU - Litvak, Nelly

AU - Donato, Debora

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N2 - 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.

AB - 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.

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KW - MSC-60J80

KW - METIS-245912

KW - MSC-90B15

KW - IR-62095

KW - MSC-68P10

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M3 - Conference contribution

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BT - Algorithms and Models for the Web-Graph

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Volkovich Y, Litvak N, Donato D. Determining factors behind the pagerank log-log plot. In Bonato A, Chung FRK, editors, Algorithms and Models for the Web-Graph: 5th International Workshop, WAW 2007, San Diego, CA, USA, December 11-12, 2007. Proceedings. Berlin, Heidelberg: Springer. 2007. p. 108-123. (Lecture Notes in Computer Science). https://doi.org/10.1007/978-3-540-77004-6_9