We consider a broad class of random bipartite networks, the distribution of which is invariant under permutation within each type of nodes. We are interested in $U$-statistics defined on the adjacency matrix of such a network, for which we define a new type of Hoeffding decomposition. This decomposition enables us to characterize non-degenerate $U$-statistics -- which are then asymptotically normal -- and provides us with a natural and easy-to-implement estimator of their asymptotic variance. \\ We illustrate the use of this general approach on some typical random graph models and use it to estimate or test some quantities characterizing the topology of the associated network. We also assess the accuracy and the power of the proposed estimates or tests, via a simulation study.

翻译：我们考虑一大类随机二分网络，其分布在每种类型节点内部具有置换不变性。我们关注定义在该类网络邻接矩阵上的$U$-统计量，并为其定义了一种新型Hoeffding分解。该分解使我们能够刻画非退化$U$-统计量（其渐近服从正态分布），并为其渐近方差提供了一种自然且易于实现的估计量。我们通过若干典型随机图模型展示了这一通用方法的应用，并利用它估计或检验了相关网络拓扑结构的某些特征量。通过模拟研究，我们还评估了所提出估计或检验的准确性和功效。