Clustering spatial networks through latent mixture models

We consider a Bayesian model-based clustering technique that directly accounts for network relations between territorial units and their position in a geographical space. This proposal is motivated by a practical problem: to design administrative structures that are intermediate between the municipality and the province within an Italian region based on the existence of a relatively (to population) high commuting flow. In our social network model, the commuting flows are explained by the distances between the municipalities, i.e., the nodes, in a 3-dimensional space, where the 2 actual geographical coordinates and the third latent variable are modelled through a Gaussian mixture.