  Ensembles of networks arise in various fields where multiple independent
networks are observed on the same set of nodes, for example, a collection of
brain networks constructed on the same brain regions for different individuals.
However, there are few models that describe both the variations and
characteristics of networks in an ensemble at the same time. In this paper, we
propose to model the ensemble of networks using a Dirichlet Process Mixture of
Exponential Random Graph Models (DPM-ERGMs), which divides the ensemble into
different clusters and models each cluster of networks using a separate
Exponential Random Graph Model (ERGM). By employing a Dirichlet process
mixture, the number of clusters can be determined automatically and changed
adaptively with the data provided. Moreover, in order to perform full Bayesian
inference for DPM-ERGMs, we employ the intermediate importance sampling
technique inside the Metropolis-within-slice sampling scheme, which addressed
the problem of sampling from the intractable ERGMs on an infinite sample space.
We also demonstrate the performance of DPM-ERGMs with both simulated and real
datasets.
