Finite Mixtures of ERGMs for Modeling Ensembles of Networks

TL;DR

This paper introduces a Bayesian framework using finite mixtures of ERGMs to model, cluster, and analyze ensembles of networks, effectively capturing heterogeneity and dependence in complex graph data.

Contribution

It proposes a novel mixture model for network ensembles with a Bayesian inference algorithm, enabling identification of latent generative mechanisms and model-based clustering.

Findings

The method accurately recovers the number of latent processes in simulations.

It effectively clusters networks based on underlying generative mechanisms.

Application to political co-voting networks demonstrates practical utility.

Abstract

Ensembles of networks arise in many scientific fields, but there are few statistical tools for inferring their generative processes, particularly in the presence of both dyadic dependence and cross-graph heterogeneity. To fill in this gap, we propose characterizing network ensembles via finite mixtures of exponential family random graph models, a framework for parametric statistical modeling of graphs that has been successful in explicitly modeling the complex stochastic processes that govern the structure of edges in a network. Our proposed modeling framework can also be used for applications such as model-based clustering of ensembles of networks and density estimation for complex graph distributions. We develop a Metropolis-within-Gibbs algorithm to conduct fully Bayesian inference and adapt a version of deviance information criterion for missing data models to choose the number of latent heterogeneous generative mechanisms. Simulation studies show that the proposed procedure can recover the true number of latent heterogeneous generative processes and corresponding parameters. We demonstrate the utility of the proposed approach using an ensemble of political co-voting networks among U.S. Senators.