Markov chain Monte Carlo exact inference for social networks

The uniformly most powerful unbiased test of reciprocity compares the observed number of mutual relations to its exact conditional distribution. Metropolis–Hastings algorithms have been proposed for generating from this distribution in order to perform Monte Carlo exact inference. Triad census statistics are often used to test for the presence of network group structure. We show how one of the proposed Metropolis–Hastings algorithms can be modified to generate from the conditional distribution of the triad census given the in-degrees, the out-degrees and the number of mutual dyads. We compare the results of this algorithm with those obtained by using various approximations.