A dynamic process interpretation of the sparse ERGM reference model

ABSTRACT

Exponential family random graph models (ERGMs) can be understood in terms of a set of structural biases that act on an underlying reference distribution. This distribution determines many aspects of the behavior and interpretation of the ERGM families incorporating it. One important innovation in this area has been the development of an ERGM reference model that produces realistic behavior when generalized to sparse networks of varying sizes. Here, we show that this model can be derived from a latent dynamic process in which tie formation takes place within small local settings between which individuals move. This derivation provides one possible micro-process interpretation of the sparse ERGM reference model and sheds light on the conditions under which constant mean degree scaling can emerge.

KEYWORDS:

• Baseline models
• ERGMs
• network dynamics
• reference measures

Notes

¹ This is conventionally done by the use of offset terms (see, e.g., Krivitsky & Kolaczyk, 2015) that deterministically alter the elements of .

² We make no particular assumptions here about the dimension of the space, or the metric with respect to which the volume is defined.

Additional information

Funding

This work was supported by National Science Foundation Division of Mathematical Sciences award DMS-13614225.