Community detection for weighted bipartite networks

TL;DR

This paper introduces a new model and spectral algorithms for community detection in weighted bipartite networks, overcoming limitations of previous models that ignored edge weights and distribution assumptions.

Contribution

The paper proposes a distribution-free bipartite model and spectral algorithms with theoretical guarantees for community detection in weighted bipartite networks.

Findings

Effective community detection in weighted bipartite networks demonstrated.

Spectral algorithms show consistent estimation of node labels.

Model extends previous binary bipartite models to weighted cases.

Abstract

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.