A Perfect Sampling Method for Exponential Family Random Graph Models

TL;DR

This paper introduces a perfect sampling method for exponential family random graph models using Coupling From The Past, enabling exact generation of graphs with complex dependencies.

Contribution

It presents a novel perfect sampling technique applicable to exponential family random graph models and demonstrates its use on Markov and biased net graph models.

Findings

Successful application to Markov graphs.

Extension to biased net models.

Efficient exact sampling from complex graph models.

Abstract

Generation of deviates from random graph models with non-trivial edge dependence is an increasingly important problem. Here, we introduce a method which allows perfect sampling from random graph models in exponential family form ("exponential family random graph" models), using a variant of Coupling From The Past. We illustrate the use of the method via an application to the Markov graphs, a family that has been the subject of considerable research. We also show how the method can be applied to a variant of the biased net models, which are not exponentially parameterized.