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On the equivalence of the edge/isolate and edge/concurrent tie ERGM families, and their extensions

ABSTRACT Partnership concurrency is a major driver of permeability of social networks to diffusion, and an important modeling target in the context of sexually transmitted infections. A seemingly unrelated phenomenon of concern in modeling social networks is isolation avoidance—the tendency of individuals to maintain at least one tie. Although concurrency bias and bias in isolate formation would naively seem to be distinct, we here show that their respective ERGM expressions (edge/concurrent tie and edge/isolate families, and their regular extensions) are equivalent, and that both are equivalent to a special case of the geometrically weighted degree families. In addition to being statistically useful, this equivalence provides insight into the essential connection between these apparently different structural phenomena.