Limiting behavior of anomalous edges in exchangeable random graphs

Community structures are a common feature of many social networks. Anomalous edges are those edges that fall between distinct communities. According to a given network with two communities, random graphs are generated by assuming that the communities of vertices are exchangeable. In this paper, under some restriction conditions, the asymptotic normality of the number of anomalous edges in such random graphs is established as the graph size tends to infinity, where the method of transforming weak convergence into conditional weak convergence on the basis of stochastic monotonicity is utilized.