  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.
