A note on perfect simulation for exponential random graph models

TL;DR

This paper introduces a perfect simulation algorithm for exponential random graph models using Coupling From The Past, proving monotonicity in certain parameters and providing bounds on the algorithm's running time.

Contribution

It presents a novel perfect simulation method for ERGMs based on Glauber dynamics and establishes conditions for monotonicity and efficiency.

Findings

Proposed a perfect simulation algorithm for ERGMs.

Proved monotonicity of ERGMs in a subset of parameters.

Derived an upper bound on the algorithm's running time.

Abstract

In this paper we propose a perfect simulation algorithm for the Exponential Random Graph Model, based on the Coupling From The Past method of Propp & Wilson (1996). We use a Glauber dynamics to construct the Markov Chain and we prove the monotonicity of the ERGM for a subset of the parametric space. We also obtain an upper bound on the running time of the algorithm that depends on the mixing time of the Markov chain.