Dynamic networks are a general language for describing time-evolving complex systems, and discrete time network models provide an emerging statistical technique for various applications. It is a fundamental research question to detect a set of nodes sharing similar connectivity patterns in time-evolving networks. Our work is primarily motivated by detecting groups based on interesting features of the time-evolving networks (e.g., stability). In this work, we propose a model-based clustering framework for time-evolving networks based on discrete time exponential-family random graph models, which simultaneously allows both modeling and detecting group structure. To choose the number of groups, we use the conditional likelihood to construct an effective model selection criterion. Furthermore, we propose an efficient variational expectation-maximization (EM) algorithm to find approximate maximum likelihood estimates of network parameters and mixing proportions. The power of our method is demonstrated in simulation studies and empirical applications to international trade networks and the collaboration networks of a large research university.
Keywords: Minorization-maximization; Model selection; Model-based clustering; Temporal ERGM; Time-evolving network; Variational EM algorithm.