Information Theoretic Comparison of Stochastic Graph Models: Some Experiments
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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- 1.Chung, F., Lu, L.: Complex Graphs and Networks (Cbms Regional Conference Series in Mathematics). American Mathematical Society (August 2006)Google Scholar
- 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
- 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.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.Blitzstein, J., Diaconis, P.: A sequential importance sampling algorithm for generating random graphs with prescribed degrees. Technical report, Stanford (2005)Google Scholar