Formation of Social Network Structure
Dean Lusher and Garry Robins
Tie Formation: Emergence of Structure
It is not always recognized that an exponential random graph model (ERGM) carries theory in the form of assumptions about networks, network processes, and social structures. We can think of “ERGM theory” as network metatheory because it is not specific to a particular network process. It is a theoretical perspective within which more specific network theories may be investigated. The essence of ERGM theory is the formation of social structure through the accumulation of small local substructures and, ultimately, through the formation of individual ties into the patterns of those substructures.
Formation of Social Ties
ERGMs are first and foremost concerned with explaining the patterns of ties in a social network. This tie-based approach of ERGMs permits answers to some questions but not others. A standard ERGM is not a model focused on predicting outcomes for individuals in the network (so called diffusion or social influence models); instead, it is about revealing patterns that may enable inferences on tie formation processes, including social selection processes where network ties are predicted from the attributes of the network actors.
Of course, there are many network theories about tie formation or tie patterning that can be drawn on in specifying an ERGM for a given network. For instance, reciprocity or exchange is seen as a basic and universal human activity (Blau, 1964), so that, generally, in human social networks we expect ties to be reciprocated. Beyond dyads, the importance of triadic relations was proposed by Simmel (1950). Following Heider (1958), Cartwright and Harary (1956) introduced structural balance theory, providing a graph theoretical approach to triangulation among social network ties, otherwise known as “path closure” or “network closure.” Since then, network closure has become a central theme in social network research. Granovetter (1973) contrasted closure of strong ties with nonclosure of weak ties. Burt (1992) examined network brokerage and structural holes, suggesting that the person in the center of a nonclosed structure is advantaged. In contrast to closure, theories of prominence in networks also suggest that people who are socially well connected may be advantaged or have distinctive status (Bavelas, 1950; Freeman, 1977, 1979). Preferential attachment describes how network popularity may induce further popularity (Barabasi & Albert, 1999; Merton, 1968; Yule, 1925), resulting in some high-degree actors in the network. In regard to actor attributes, the importance of homophily has been well documented (McPherson, Smith-Lovin, & Cook, 2001) as a means to explain the presence of network ties. For multiple networks with different types of tie, Nadel (1952) and White (2008) suggested one social network could provide a context for another, so that there may be interdependencies across different networks, whereby ties in one network might encourage the formation of ties in another.
-  An ERGM-type approach can be used for social influence models, however (see Chapter 9).