Nowicki, Krzysztof, Asymptotic Poisson distributions with applications to statistical analysis of graphs, Advances in applied probability , 20(2), 1988, pp. 315-330
Various types of graph statistics for graphs and digraphs are presented as numerators of incomplete U-statistics, with symmetric and asymmetric kernels, respectively. Thus, asymptotic Poisson limits of these statistics are provided by using limit theorems for the sums of dissociated random variables. Several applications to statistical analysis of graphs are given.