The Pairwise Prony Algorithm: Efficient Inference of Stochastic Block Models with Prescribed Subgraph Densities

We present an elegant and flexible algorithm that provides the parameters of the simplest stochastic block model (SBM) for a given set of prescribed subgraph densities, from which one can sample networks with negligible computational overhead. The method generalizes the classical method of Prony to the pairwise data of networks. The class of inferred models are at the intersection of exponential random graph models (ERGMs), which are characterized in terms of maximum entropy, and of exchangeable random graphs (i.e., graphons). We show that the required subgraph densities can be efficiently computed for both dense and sparse networks, and provide an implementation of our algorithm in python. Our method provides standardized null models for statistical analysis of network data, including for the challenging case of a single observed graph.