Weighted Exponential Random graph models: Scope and large network limits

TL;DR

This paper analyzes weighted exponential random graph models in large networks, deriving their limiting structure and conditions for continuity, with applications to socio-economic and neuroscience data.

Contribution

It extends fundamental results of unweighted ERGMs to weighted models, including unbounded measures and nodal covariates, and discusses open problems.

Findings

Derived limiting results for weighted ERGMs as network size grows.

Established conditions for continuity of model functionals.

Applicable to diverse measures, including unbounded support.

Abstract

We study models of weighted exponential random graphs in the large network limit. These models have recently been proposed to model weighted network data arising from a host of applications including socio-econometric data such as migration flows and neuroscience. Analogous to fundamental results derived for standard (unweighted) exponential random graph models in the work of Chatterjee and Diaconis, we derive limiting results for the structure of these models as the number of nodes goes to infinity. Our results are applicable for a wide variety of base measures including measures with unbounded support. We also derive sufficient conditions for continuity of functionals in the specification of the model including conditions on nodal covariates. Finally we include a number of open problems to spur further understanding of this model especially in the context of applications.