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.
Barber REF extended the definition of Newman's modularityin unipartite network to be appropriate for bipartite networks and presents a bipartite modularity based on the assumption that there is a one-to-one correspondence between communities of different node type.
Modularity and community detection in bipartite networks
Phys. Rev. E 76, 066102 (2007)
Medicine Mathematics Physics