Introduction to exponential random graph models

Abstract

Exponential random graph models (ERGMs) are used for analyzing network data for a variety of applications. Vertices, or nodes, represent entities, and edges, or ties, represent connections between entities. The ERGM model allows for a representation of edges in structures (from lone edges to triangles and cycles) as an exponential family random variable, a known family of distributions with known properties, such as showing statistics to be complete or sufficient by viewing the distribution. This paper provides an introduction to the topic with both theoretical and applied information, starting with an introduction to the necessary graph theory, graph structures, and theoretical background for fitting models, then moves on to worked examples using the Statnet package.