  We construct a novel class of stochastic blockmodels using Bayesian
nonparametric mixtures. These model allows us to jointly estimate the structure
of multiple networks and explicitly compare the community structures underlying
them, while allowing us to capture realistic properties of the underlying
networks. Inference is carried out using MCMC algorithms that incorporates
sequentially allocated split-merge steps to improve mixing. The models are
illustrated using a simulation study and a variety of real-life examples.
