  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.
