A Perfect Sampling Method for Exponential Random Graph Models

Generation of deviates from random graph models with non-trivial edge dependence is an increasingly important problem in the social and biological sciences. In recent years, work on this problem has been greatly facilitated by the use of discrete exponential families to parameterize random graph models, and by the availability of associated Markov chain Monte Carlo methods for approximate simulation of these families. Here, we introduce a method which allows perfect sampling from random graph models in exponential family form (aka "exponential 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 of considerable importance within the social network literature. Applications of the method to other common cases (including the non-exponentially parameterized biased net models) are also discussed.