Clustering Time-Evolving Networks Using Temporal Exponential-Family Random Graph Models with Conditional Dyadic Independence and Dynamic Latent Blocks

Model-based clustering of dynamic networks has emerged as an increasingly important research topic in statistical network analysis. Effectively and efficiently exploring the dynamic latent block structure of time-evolving networks is critical. We propose a statistical clustering framework based on temporal exponential-family random graph models (ERGMs) with conditional dyadic independence and a hidden Markov structure. These conditional independent temporal ERGMs allow for the specification of meaningful network features, while the hidden Markov structure helps infer the dynamic latent block structure. Additionally, we develop a variational expectation-maximization algorithm to approximate maximum likelihood estimation and present an effective model selection criterion, based on the integrated classification likelihood, to determine the optimal number of clusters. Finally, we demonstrate the numerical performance of our proposed method through extensive simulation studies and real-world applications. Supplementary materials for this article are available online.