Hierarchical Community Detection in Bipartite Networks

TL;DR

This paper introduces a new modularity-based method, Qbg, for detecting hierarchical communities in bipartite networks, effectively handling weighted systems and revealing multi-scale structures.

Contribution

It presents a novel objective function, Qbg, that enables systematic exploration of hierarchical community structures in bipartite networks without network projection.

Findings

Qbg accurately recovers known mesoscale structures

Reveals additional hierarchical and fine-scale organization

Effective on both synthetic and empirical bipartite networks

Abstract

Many bipartite networks exhibit hierarchical community structure, but existing community detection methods are not well-suited for detecting hierarchy. They also do not effectively handle weighted bipartite networks. In this work, we introduce a novel modularity-based objective function, called the generalized bipartite modularity density, Qbg, specifically designed for hierarchical community detection in bipartite systems. The framework incorporates a tunable resolution parameter that enables systematic exploration of community structure across multiple scales. It leverages resolution-limit behavior in bipartite networks as a tool to uncover hierarchical organization without projecting the network or altering its intrinsic bipartite topology. We evaluate the method using a hierarchical synthetic bipartite benchmark and apply it to two empirical networks. In all cases, Qbg recovers established mesoscale structure while revealing additional hierarchical and fine-scale organization beyond that detected by conventional bipartite approaches. These results establish Qbg as a flexible, interpretable, and resolution-aware framework for hierarchical community detection in bipartite networks.