Abstract

Exponential random graph models (ERGM) is a family of statistical distributions for ties in a social network. The inferential goal is to explain the mechanisms of tie-formation in networks such as why some people collaborate and others don’t. A fundamental aspect of most tie-formation processes is that relational ties do not form independently of each other. ERGM models the occurrence of ties between nodes as a collection of binary random variables. Dependencies between ties are modelled by interaction terms as in log-linear models. This entry describes how these interaction terms represent substantively meaningful configurations capturing fundamental network processes, and the history behind how these have been derived from theoretical as well as technical considerations. How these configurations, or statistics, are defined for different types of network structures is elaborated with reference to specific classes of dependence assumptions. Fundamental aspects of estimating and fitting ERGMs are discussed and applied worked examples are provided. This exposition highlights the ways in which ERGMs differ from what may be called standard statistical models in the social and behavioural sciences.