Complex Combination of Multiple and Nested Social Processes

It is important to note that the tie-based approach of ERGMs permits an understanding of the “complex combination” of social processes by which network ties are formed. We point to multiple and nested processes.

Multiple Origins of Social Network Structure. Previously in this chapter, we presented a number of theories about the formation of network ties, without attempting a complete list. However, it would be a brave person who would suggest that one and only one of these processes explains all there is to know about the organization of a social network. The totality of ties in a network is not likely to be explained only by homophily, or only by reciprocity, but it is certainly feasible that both processes may be at play at the same time within the one network. By incorporating a number of configurations simultaneously into a model (such as one for homophily and one for reciprocity), an ERGM can test the evidence as to which processes contribute to the formation of the network structure (Monge & Contractor, 2003).

Nested configurations for a transitive triad

Figure 3.2. Nested configurations for a transitive triad.

In the one social network, there is no a priori reason why multiple social processes should not be present. Because humans are intentional beings with multiple motivations for and multiple expressions of social action, it is especially in human social networks that we expect that multiple processes will occur simultaneously. Of course, we do need to be guided by theory, and we certainly need to be empirical, but expecting a simple explanation for a complex human social system is naive.

Nested Configurations. It is important to realize that configurations are often nested within one another. The simplest network configuration is a single network tie. Every other configuration obviously contains this configuration, and possibly others. Consider a transitive triad. This configuration includes within it three single arcs: one 2-path, one out-2-star, and one in-2-star (see Figure 3.2 for a depiction of these configurations).

Because configurations are nested in one another, it is not enough, for instance, to observe many triangles to infer an effect for network closure. There may be many triangles because there are many ties (i.e., the network is dense), or because there are many 2-paths or 2-stars (i.e., in- and out-2-stars for directed networks). To have solid evidence of network closure, we need to observe more than expected triangles given (i.e., taking into consideration) the number of 2-paths (and arcs and 2-stars) in the data.

Given an average baseline propensity to form arcs, if that propensity is strong enough, we will see some transitive triads simply by chance. The stronger the baseline effect, the more transitive triads. The same applies if there are propensities to form 2-stars and 2-paths. Thus, we can only infer a specific process of transitive closure by considering the propensities for the four lower-order configurations and a transitivity effect simultaneously. We ask, do we see more transitive triads in the

network data than we expect to see given the average tendency to form arcs, 2-stars, and 2-paths? If so, we have evidence for a transitive closure effect. If not, then the presence of transitive triads in the network can be explained more simply by the presence of the lower-order configurations, and we do not need to postulate a closure effect to explain this network structure.

In summary, when we talk of multiple processes, it is not just that there are many choices. Rather, local, multiple, and nested network effects combine into a complex combination of processes. ERGMs are about understanding the complexity of a social system - its multiplicity, its interconnectedness, and its dependencies.

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