Normal approximation for generalized<i>U</i>-statistics and weighted random graphs

We derive normal approximation bounds in the Wasserstein distance for sums of generalized U-statistics, based on a general bound functionals independent random variables arbitrary distributions. Those are applied to combined weights subgraphs Erdős–Rényi graph, extending graph counting results Barbour et al. (A central limit theorem decomposable with applications graphs, J. Combin. Theory Ser. B 47(2) (1989), pp. 125–145) setting weighted graphs. Our approach relies stochastic analytic framework sequences.