Co-modularity and Detection of Co-communities

This paper introduces the notion of co-modularity, to co-cluster observations of bipartite networks into co-communities. The task of co-clustering is to group together nodes of one type, whose interaction with nodes of another type are the most similar. The novel measure of co-modularity is introduced to assess the strength of co-communities, as well as to arrange the representation of nodes and clusters for visualisation, and to define an objective function for optimisation. We illustrate the power of our proposed methodology on simulated data, as well as with examples from genomics and consumer-product reviews.