We explore data from the neuronal network of the nematode C. elegans, a tiny hermaphroditic roundworm. The data consist of 279 neurons and 5863 directed connections between them, represented by three connectomes of electrical and chemical synapses. Our approach uses a fully Bayesian two-stage clustering method, based on the Dirichlet processes, that borrows information across the connectomes to identify communities of neurons via stochastic block modeling. This structure allows us to understand the communication patterns between the motor neurons, interneurons, and sensory neurons of the C. elegans nervous system.