A Bayesian Approach to Network Modularity

We present an efficient, principled, and interpretable technique for inferring module assignments and identifying the optimal number of modules in a given network. We show how several existing methods for finding modules can be described as variant, special, or limiting cases of our work, and how related methods for complexity control -- identification of the true number of modules -- are outperformed. Our approach is based on Bayesian methods for model selection which have been used with success for almost a century, implemented using a variational technique developed only in the past decade. We apply the technique to synthetic and real networks, including networks of up to $10^4$ nodes, and outline how the method naturally allows model selection among generative models.