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 Block Model of Nowicki & Snijders (2001) and make use of modern techniques such as collapsing, and using conjugate priors where necessary, allowing us to avoid the need for transdimensional MCMC. This gives a model which is simpler to work with and which enables the use of faster algorithms. The algorithm is based on the allocation sampler of Nobile & Fearnside (2007), and this algorithm, along with the extensions in our model, allows us to directly estimate the number of clusters. 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.
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