Bipartite networks are a natural representation of the interactions between entities from two different types. The organization (or topology) of such networks gives insight to understand the systems they describe as a whole. Here, we rely on motifs which provide a meso-scale description of the topology. Moreover, we consider the bipartite expected degree distribution (B-EDD) model which accounts for both the density of the network and possible imbalances between the degrees of the nodes. Under the B-EDD model, we prove the asymptotic normality of the count of any given motif, considering sparsity conditions. We also provide close-form expressions for the mean and the variance of this count. This allows to avoid computationally prohibitive resampling procedures. Based on these results, we define a goodness-of-fit test for the B-EDD model and propose a family of tests for network comparisons. We assess the asymptotic normality of the test statistics and the power of the proposed tests on synthetic experiments and illustrate their use on ecological data sets.

翻译：二分网络是两种不同类型实体间相互作用的自然表示。此类网络的拓扑结构有助于从整体上理解其所描述的系统。本文基于模体（motif）展开研究，这类模体提供了拓扑结构的中尺度描述。此外，我们考虑了二分期望度分布（B-EDD）模型，该模型同时兼顾网络密度与节点度可能存在的失衡。在B-EDD模型框架下，考虑稀疏性条件，我们证明了任意给定模体计数的渐近正态性。我们还给出了该计数均值与方差的闭式表达式，从而避免了计算成本高昂的重采样过程。基于这些结果，我们定义了B-EDD模型的拟合优度检验，并提出了一族用于网络比较的检验方法。我们通过合成实验评估了检验统计量的渐近正态性及所提检验的检验力，并在生态数据集上展示了其应用。