The Hierarchical Stochastic Block Model for Replicated Networks

In many research fields, there is an increased availability of network data arising as replicated networks. However, most statistical models for network data in the literature are designed for a single network. Among these, the Stochastic Block Model is arguably the most popular model to perform vertex clustering and community detection. We propose the Hierarchical Stochastic Block Model, a generalization of the SBM to the setting of replicated networks. This model uses a Hierarchical Pitman-Yor prior for the block allocation vector of each graph, and allows different networks to share the same latent blocks. The number of blocks in each graph and the overall number of blocks need not be specify by the practitioner, hence avoiding complicated model selection procedures. A novel MCMC algorithm to perform posterior inference is derived. To illustrate how the model is able to capture different levels of block sharing, the HSBM is fit to a co-authorship and a brain connectomic network.