Stochastic Block Smooth Graphon Model

Abstract: The paper proposes the combination of stochastic blockmodels with smooth graphon models. The first allow for partitioning the set of individuals in a network into blocks which represent groups of nodes that presumably connect stochastically equivalently, therefore often also called communities. Smooth graphon models instead assume that the network's nodes can be arranged on a one-dimensional scale such that closeness implies a similar connectivity behavior. Both models belong to the model class of node-specific latent variables, entailing a natural relationship. While these model strands have developed more or less completely independently, this paper proposes their generalization towards stochastic block smooth graphon models. This approach enables to exploit the advantages of both worlds. We pursue a general EM-type algorithm for estimation and demonstrate the usability by applying the model to both simulated and real-world examples.