A Dynamic Process Interpretation of the Sparse ERGM Reference Model

TL;DR

This paper offers a dynamic process perspective on the sparse ERGM reference model, explaining its behavior through a latent tie formation process in local settings, and clarifying conditions for mean degree scaling in sparse networks.

Contribution

It introduces a micro-process interpretation of the sparse ERGM reference model based on a latent dynamic process of tie formation.

Findings

Derives the sparse ERGM reference model from a latent dynamic process.

Provides conditions under which constant mean degree scaling emerges.

Enhances understanding of structural biases in sparse network models.

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 size. 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.