Continuous Time Graph Processes with Known ERGM Equilibria: Contextual Review, Extensions, and Synthesis

TL;DR

This paper reviews continuous-time graph processes that converge to known ERGM distributions, discusses conditions for convergence, and introduces novel process examples and extensions within this framework.

Contribution

It provides a comprehensive review of convergence conditions, introduces new process examples, and extends existing models to continuous time with ERGM equilibria.

Findings

Conditions for convergence to ERGM distributions

Examples of novel continuous-time graph processes

Extensions of temporal exponential family models

Abstract

Graph processes that unfold in continuous time are of obvious theoretical and practical interest. Particularly useful are those whose long-term behavior converges to a graph distribution of known form. Here, we review some of the conditions for such convergence, and provide examples of novel and/or known processes that do so. These include subfamilies of the well-known stochastic actor oriented models, as well as continuum extensions of temporal and separable temporal exponential family random graph models. We also comment on some related threads in the broader work on network dynamics, which provide additional context for the continuous time case.