  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 the community structure in time-evolving networks. However, due to
significant computational challenges and difficulties in modeling communities
of time-evolving networks, there is little progress in the current literature
to effectively find communities in time-evolving networks. In this work, we
propose a novel model-based clustering framework for time-evolving networks
based on discrete time exponential-family random graph models. To choose the
number of communities, we use 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. By using variational
methods and minorization-maximization (MM) techniques, our method has appealing
scalability for large-scale time-evolving networks. The power of our method is
demonstrated in simulation studies and empirical applications to international
trade networks and the collaboration networks of a large American research
university.
