The Graph Pencil Method: Mapping Subgraph Densities to Stochastic Block Models

Lee M. Gunderson, Gecia Bravo-Hermsdorff, Peter Orbanz

Keywords: Stochastic block model, SBM, graphons, matrix pencil method, method of moments

TL;DR: We propose the graph pencil method: an elegant and efficient procedure for inferring a stochastic block model (SBM) from prescribed subgraph densities.

Abstract: In this work, we describe a method that determines an exact map from a finite set of subgraph densities to the parameters of a stochastic block model (SBM) matching these densities. Given a number K of blocks, the subgraph densities of a finite number of stars and bistars uniquely determines a single element of the class of all degree-separated stochastic block models with K blocks. Our method makes it possible to translate estimates of these subgraph densities into model parameters, and hence to use subgraph densities directly for inference. The computational overhead is negligible; computing the translation map is polynomial in K, but independent of the graph size once the subgraph densities are given.

Submission Number: 12523