Information Theoretic Comparison of Stochastic Graph Models: Some Experiments

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.KeywordsRandom GraphDegree DistributionCluster StructureDegree SequenceReal GraphThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.