Community Detection with the Canonical Ensemble
For network analysts, this offers a principled way to test hypotheses about community structure, but the method is demonstrated only on small-scale examples without quantitative performance comparisons.
The authors reformulate community detection as a hypothesis testing problem, using a z-score-like statistic and canonical ensemble null models to test for specific community structures, providing more definitive answers than generic algorithms.
Network community detection is usually considered as an unsupervised learning problem. Given a network, the aim is to partition it using some general purpose algorithm. In this paper we instead treat community detection as a hypothesis testing problem. Given a network, we examine the evidence for specific community structure in the observed network compared to a null model. To do this we define an appropriate test statistic, analogous to a z-score, and several null models derived from maximising entropy under different constraints in the canonical ensemble. We demonstrate the application of this method on real and synthetic data and contrast our method to Bayesian approaches based on the stochastic block model. We demonstrate that this method gives definitive answers to concrete questions, which can be more useful to analysts than the output of a generic algorithm.