Modularity and community detection in bipartite networks

TLDR

Modularity measures how strongly vertices cluster into communities compared to a null model network. The study introduces a bipartite‑specific null model and uses it to define a modularity metric for bipartite networks. Bipartite modularity is expressed through a modularity matrix B, whose eigenspectrum properties guide an algorithm that assigns modules by mutually inducing vertices across the two network parts. When applied to real‑world data, the algorithm accurately recovers the modular structure of bipartite networks.

Abstract

The modularity of a network quantifies the extent, relative to a null model network, to which vertices cluster into community groups. We define a null model appropriate for bipartite networks, and use it to define a bipartite modularity. The bipartite modularity is presented in terms of a modularity matrix B; some key properties of the eigenspectrum of B are identified and used to describe an algorithm for identifying modules in bipartite networks. The algorithm is based on the idea that the modules in the two parts of the network are dependent, with each part mutually being used to induce the vertices for the other part into the modules. We apply the algorithm to real-world network data, showing that the algorithm successfully identifies the modular structure of bipartite networks.