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.

中文翻译：

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关于边缘/隔离和边缘/并发连接 ERGM 族的等价性及其扩展

摘要 合作伙伴并发性是社交网络传播渗透性的主要驱动力，也是性传播感染背景下的重要建模目标。在社交网络建模中，一个看似无关的关注现象是隔离回避——个人倾向于至少保持一条联系。尽管并发偏差和隔离形成中的偏差看起来很天真，但我们在这里表明它们各自的 ERGM 表达式（边缘/并发连接和边缘/隔离系列，以及它们的常规扩展）是等效的，并且两者都等效于一个特殊的几何加权度族的情况。除了在统计上有用之外，这种等价性还提供了对这些明显不同的结构现象之间的基本联系的洞察。