Draft not to be quotedMARKOV CHAIN MONTE CARLO EXACT METHODSFOR ANALYZING SOCIAL NETWORK

A test of reciprocity is often performed by analysts of social network data. This test corresponds to testing whether a parameter in an exponential family model for the adjacency matrix is zero. The uniformly most powerful unbiased test compares the observed number of mutual relations in the social network to its exact conditional distribution. As this distribution is typically only known to a constant of proportionality, we propose a Metropolis-Hastings algorithm for generating from this distribution. We compare the results of our algorithm with those obtained by enumeration and importance sampling.