The bipartite network appears in various areas, such as biology, sociology, physiology, and computer science. \cite{rohe2016co} proposed Stochastic co-Blockmodel (ScBM) as a tool for detecting community structure of binary bipartite graph data in network studies. However, ScBM completely ignores edge weight and is unable to explain the block structure of a weighted bipartite network. Here, to model a weighted bipartite network, we introduce a Bipartite Distribution-Free model by releasing ScBM's distribution restriction. We also build an extension of the proposed model by considering the variation of node degree. Our models do not require a specific distribution on generating elements of the adjacency matrix but only a block structure on the expected adjacency matrix. Spectral algorithms with theoretical guarantees on the consistent estimation of node labels are presented to identify communities. Our proposed methods are illustrated by simulated and empirical examples.

翻译：二分网络广泛存在于生物学、社会学、生理学和计算机科学等领域。cite{rohe2016co}提出了随机共块模型（ScBM），用于检测网络研究中二元二分图数据的社区结构。然而，ScBM完全忽略了边的权重，无法解释加权二分网络的块结构。本文为建模加权二分网络，通过放宽ScBM的分布约束，引入了二分无分布模型。我们还通过考虑节点度的变异性对该模型进行了扩展。我们的模型不要求邻接矩阵元素生成服从特定分布，仅要求期望邻接矩阵具有块结构。我们提出了具有节点标签一致估计理论保证的谱算法来识别社区。通过模拟和实证案例展示了所提方法的有效性。