Keywords: dynamic networks, temporal exponential-family random graph model, hidden Markov model, variational inference, model selection
Model-based clustering of dynamic networks has emerged as an essential research topic in statistical network analysis. It is critical to effectively and efficiently model the time-evolving latent block structure of dynamic networks in practice. We present a principled statistical clustering of dynamic networks through the temporal exponential-family random graph models with a hidden Markov structure. The temporal exponential-family random graph models allow us to detect groups based on interesting features of the dynamic networks and the hidden Markov structure is used to infer the time-evolving block structure of dynamic networks. We prove the identification conditions for both network parameters and transition matrix in our proposed model-based clustering. We propose an effective model selection criterion based on the integrated classification likelihood for choosing an appropriate number of clusters. We develop a variational expectation-maximization algorithm to solve the approximate maximum likelihood estimate. The numerical performance of our proposed method is demonstrated in simulation studies and real data applications.