Exponential Random Graph Models

Abstract

This article describes a class of log-linear models for statistical analysis of social network data commonly referred to as exponential random graph (ERG) models. ERG mod- els are appropriate when one wishes to model the ties among pairs of nodes in a graph as a collection of binary outcome variables. Based on a set of dependence assumptions for how the tie variables are associated, the ERG model can be expressed as an exponential family distribution in canonical form with graph statistics that take the form of local configurations. The ERG model is introduced in its basic form, and the current estimation strategies are presented. Extensions of ERG and current challenges are briefly discusse..