Exponential Random Graph Models

Relationships are central to peoples’ health and well-being—humans are hardwired to be social. Through relationships, people gain access to resources, which can take the form of support, information, ideas, or advice, among others. Moreover, relationships benefit not just the individual but also the entire group of people involved (the social network). Social network approaches give researchers an avenue to explore relationships and how resources exchanged through these relationships impact individuals and groups. This entry describes one method for exploring tie formation in networks: exponential random graph models (ERGMs). ERMGs are a family of statistical models that allow researchers to examine patterns of relationships in social networks and to explore how social processes and personal attributes of actors are related to the presence or absence of ties in the network. More succinctly, ERGMs are models for understanding the formation of social network ties.

Social networks consist of actors or nodes (e.g., people, organizations, countries) who are connected to actors via ties or relationships. Social networks can be undirected or directed. In an undirected network, a tie indicates the presence of a relationship. For example, a network of teachers in a school who work in committees is an undirected network—a tie between actors would indicate that they work in the same committee. In directed networks, ties indicate the direction of the flow of resources from one person to another. For example, a network where teachers in a school indicate which colleagues they seek for advice would be an example of a directed network. A sent tie (i.e., an actor seeking advice) is known as an outdegree; a received tie (i.e., an actor being sought for advice) is known as an indegree. The type of network—directed or undirected—has implication for modeling the formation of ties in that network. Social network approaches allow researchers to understand not only the outcomes derived from networks but also the antecedent social processes that foster tie formation in networks and how to interpret them.