In the model-based clustering of networks, blockmodelling may be used to identify roles in the network. We identify a special case of the Stochastic Block Model (SBM) where we constrain the cluster-cluster interactions such that the density inside the clusters of nodes is expected to be greater than the density between clusters. This corresponds to the intuition behind community-finding methods, where nodes tend to clustered together if they link to each other. We call this model Stochastic Community Finding (SCF) and present an efficient MCMC algorithm which can cluster the nodes, given the network. The algorithm is evaluated on synthetic data and is applied to a social network of interactions at a karate club and at a monastery, demonstrating how the SCF finds the 'ground truth' clustering where sometimes the SBM does not. The SCF is only one possible form of constraint or specialization that may be applied to the SBM. In a more supervised context, it may be appropriate to use other specializations to guide the SBM.