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.
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