A stopping rule for randomly sampling bipartite networks with fixed degree sequences

Statistical analysis of bipartite networks frequently requires randomly sampling from the set of all bipartite networks with the same degree sequence as an observed network. Trade algorithms offer an efficient way to generate samples of bipartite networks by incrementally `trading' the positions of some of their edges. However, it is difficult to know how many such trades are required to ensure that the sample is random. I propose a stopping rule that focuses on the distance between sampled networks and the observed network, and stops performing trades when this distribution stabilizes. Analyses demonstrate that, for over 650 different degree sequences, using this stopping rule ensures a random sample with a high probability, and that it is practical for use in empirical applications.