Information Theoretic Comparison of Stochastic Graph Models: Some Experiments

  • Kevin J. Lang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5427)

Abstract

The Modularity-Q measure of community structure is known to falsely ascribe community structure to random graphs, at least when it is naively applied. Although Q is motivated by a simple kind of comparison of stochastic graph models, it has been suggested that a more careful comparison in an information-theoretic framework might avoid problems like this one. Most earlier papers exploring this idea have ignored the issue of skewed degree distributions and have only done experiments on a few small graphs. By means of a large-scale experiment on over 100 large complex networks, we have found that modeling the degree distribution is essential. Once this is done, the resulting information-theoretic clustering measure does indeed avoid Q’s bad property of seeing cluster structure in random graphs.

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References

  1. 1.
    Chung, F., Lu, L.: Complex Graphs and Networks (Cbms Regional Conference Series in Mathematics). American Mathematical Society (August 2006)Google Scholar
  2. 2.
    Bezáková, I., Kalai, A., Santhanam, R.: Graph model selection using maximum likelihood. In: ICML 2006: Proceedings of the 23rd international conference on Machine learning, pp. 105–112. ACM, New York (2006)Google Scholar
  3. 3.
    Rissanen, J.: Modelling by the shortest data description. Automatica 14, 465–471 (1978)CrossRefMATHGoogle Scholar
  4. 4.
    Chakrabarti, D., Papadimitriou, S., Modha, D.S., Faloutsos, C.: Fully automatic cross-associations. In: KDD 2004: Proceedings of the tenth ACM SIGKDD international conference on Knowledge discovery and data mining, pp. 79–88. ACM, New York (2004)CrossRefGoogle Scholar
  5. 5.
    Rosvall, M., Bergstrom, C.T.: An information-theoretic framework for resolving community structure in complex networks. Proc. Natl. Acad. Sci. U S A 104(18), 7327–7331 (2007)CrossRefGoogle Scholar
  6. 6.
    Newman, M.E.J., Girvan, M.: Finding and evaluating community structure in networks. Phys. Rev. E 69, 026113 (2004)CrossRefGoogle Scholar
  7. 7.
    Guimera, R., Sales-Pardo, M., Amaral, L.A.N.: Modularity from fluctuations in random graphs and complex networks. Physical Review E 70, 025101 (2004)CrossRefGoogle Scholar
  8. 8.
    Hofman, J.M., Wiggins, C.H.: A bayesian approach to network modularity. Physical Review Letters 100, 258701 (2008)CrossRefGoogle Scholar
  9. 9.
    Boldi, P., Vigna, S.: The webgraph framework i: compression techniques. In: WWW 2004: Proceedings of the 13th international conference on World Wide Web, pp. 595–602. ACM, New York (2004)Google Scholar
  10. 10.
    Dhillon, I.S., Guan, Y., Kulis, B.: Weighted graph cuts without eigenvectors a multilevel approach. IEEE Trans. Pattern Anal. Mach. Intell. 29(11) (2007)Google Scholar
  11. 11.
    Blitzstein, J., Diaconis, P.: A sequential importance sampling algorithm for generating random graphs with prescribed degrees. Technical report, Stanford (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Kevin J. Lang
    • 1
  1. 1.Yahoo ResearchSanta ClaraUSA

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