  Networks are useful representations of many systems with interacting
entities, such as social, biological and physical systems. Characterizing the
meso-scale organization, i.e. the community structure, is an important problem
in network science. Community detection aims to partition the network into sets
of nodes that are densely connected internally but sparsely connected to other
dense sets of nodes. Current work on community detection mostly focuses on
static networks. However, many real world networks are dynamic, i.e. their
structure and properties change with time, requiring methods for dynamic
community detection. In this paper, we propose a new stochastic block model
(SBM) for modeling the evolution of community membership. Unlike existing SBMs,
the proposed model allows each community to evolve at a different rate. This
new model is used to derive a maximum a posteriori estimator for community
detection, which can be written as a constrained spectral clustering problem.
In particular, the transition probabilities for each community modify the graph
adjacency matrix at each time point. This formulation provides a relationship
between statistical network inference and spectral clustering for dynamic
networks. The proposed method is evaluated on both simulated and real dynamic
networks.

Physics and Society;Social and Information Networks