Skip to main content
SpringerLink
Log in

Characterization of Tail Dependence for In-Degree and PageRank

  • Conference paper
Algorithms and Models for the Web-Graph (WAW 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5427))

Included in the following conference series:

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.

Part of this research has been funded by the Dutch BSIK/BRICKS project. This article is also the result of joint research in the 3TU Centre of Competence NIRICT (Netherlands Institute for Research on ICT) within the Federation of Three Universities of Technology in The Netherlands.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Chakrabarti, D., Faloutsos, C.: Graph mining: Laws, generators, and algorithms. ACM Comput. Surv. 38(1), 2 (2006)

    Article  Google Scholar 

  2. Mitzenmacher, M.: A brief history of generative models for power law and lognormal distributions. Internet Math. 1(2), 226–251 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  3. Newman, M.E.J.: The structure and function of complex networks. SIAM Rev. 45(2), 167–256 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  4. Donato, D., Laura, L., Leonardi, S., Millozi, S.: Large scale properties of the Webgraph. Eur. Phys. J. 38, 239–243 (2004)

    Article  Google Scholar 

  5. Pandurangan, G., Raghavan, P., Upfal, E.: Using PageRank to characterize Web structure. In: Ibarra, O.H., Zhang, L. (eds.) COCOON 2002. LNCS, vol. 2387, p. 330. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  6. Volkovich, Y., Litvak, N., Donato, D.: Determining factors behind the PageRank log-log plot. In: Bonato, A., Chung, F.R.K. (eds.) WAW 2007. LNCS, vol. 4863, pp. 108–123. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  7. Brin, S., Page, L.: The anatomy of a large-scale hypertextual Web search engine. Comput. Networks 33, 107–117 (1998)

    Google Scholar 

  8. Fortunato, S., Boguñá, M., Flammini, A., Menczer, F.: Approximating PageRank from in-degree. In: Aiello, W., Broder, A., Janssen, J., Milios, E.E. (eds.) WAW 2006. LNCS, vol. 4936, pp. 59–71. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  9. Beirlant, J., Goegebeur, Y., Segers, J., Teugels, J.: Statistics of Extremes: Theory and Applications. Wiley, Chichester (2004)

    Book  MATH  Google Scholar 

  10. Resnick, S.I.: Heavy-tail Phenomena. Springer, New York (2007)

    MATH  Google Scholar 

  11. Volkovich, Y., Litvak, N., Zwart, B.: Measuring extremal dependencies in Web graphs. In: WWW 2008: Proceedings of the 17th international conference on World Wide Web, pp. 1113–1114. ACM Press, New York (2008)

    Google Scholar 

  12. Volkovich, Y., Litvak, N., Zwart, B.: A framework for evaluating statistical dependencies and rank correlations in power law graphs. Memorandum 1868, Enschede (2008)

    Google Scholar 

  13. Litvak, N., Scheinhardt, W.R.W., Volkovich, Y.: Probabilistic relation between in-degree and PageRank. In: Aiello, W., Broder, A., Janssen, J., Milios, E.E. (eds.) WAW 2006. LNCS, vol. 4936, pp. 72–83. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  14. Volkovich, Y., Litvak, N.: Asymptotic analysis for personalized Web search. Memorandum 1884, Enschede (2008)

    Google Scholar 

  15. Jessen, A.H., Mikosch, T.: Regularly varying functions. Publications de l’institut mathematique, Nouvelle série 79(93) (2006)

    Google Scholar 

  16. Boldi, P., Vigna, S.: The WebGraph framework I: Compression techniques. In: WWW 2004: Proceedings of the 13th International Conference on World Wide Web, pp. 595–601. ACM Press, New York (2004)

    Google Scholar 

  17. Albert, R., Barabási, A.L.: Emergence of scaling in random networks. Science 286, 509–512 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  18. Avrachenkov, K., Lebedev, D.: PageRank of scale-free growing networks. Internet Math. 3(2), 207–231 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  19. van der Hofstad, R., Hooghiemstra, G., van Mieghem, P.: Distances in random graphs with finite variance degrees. Random Structures Algorithms 27(1), 76–123 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  20. van der Hofstad, R., Hooghiemstra, G., Znamenski, D.: Distances in random graphs with finite mean and infinite variance degrees. Electron. J. Probab. 12(25), 703–766 (2007)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands

    Nelly Litvak, Werner Scheinhardt & Yana Volkovich

  2. CWI, Science Park Amsterdam, Kruislaan 413, 1098 SJ, Amsterdam, The Netherlands

    Bert Zwart

Authors
  1. Nelly Litvak
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Werner Scheinhardt
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yana Volkovich
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Bert Zwart
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. INRIA Sophia Antipolis, 2004, 06902, Route des Lucioles, France

    Konstantin Avrachenkov

  2. Yahoo! Research, Barcelona Ocata 1, 1st floor, 08003, Barcelona Catalunya, Spain

    Debora Donato

  3. Dept. of Applied Mathematics, University of Twente, P.O. Box 217, 7500AE, Enschede, The Netherlands

    Nelly Litvak

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Litvak, N., Scheinhardt, W., Volkovich, Y., Zwart, B. (2009). Characterization of Tail Dependence for In-Degree and PageRank. In: Avrachenkov, K., Donato, D., Litvak, N. (eds) Algorithms and Models for the Web-Graph. WAW 2009. Lecture Notes in Computer Science, vol 5427. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-95995-3_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-95995-3_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-95994-6

  • Online ISBN: 978-3-540-95995-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation