Clustering in networks with the collapsed Stochastic Block Model

We present an efficient MCMC algorithm to cluster the nodes of a network such that nodes with similar role in the network are clustered together. This is known as block-modelling or block-clustering. We extend the stochastic blockmodel (SBM) of Nowicki & Snijders (2001), by exploiting parameter collapsing to integrate out block parameters. The resulting model defines a posterior over the number of clusters and cluster memberships. Sampling from this model is simpler than from the original SBM as transdimensional MCMC can be avoided. Moreover, our extensions allow the number of clusters to be directly estimated, rather than given as an input parameter. The algorithm is based on the allocation sampler of Nobile & Fearnside (2007). We use synthetic and real data to test the speed and accuracy of our model and algorithm, including the ability to estimate the number of clusters. The algorithm can scale to networks with up to ten thousand nodes.