An Efficient Algorithm for Optimizing Bipartite Modularity in Bipartite Networks

Modularity evaluates the quality of a division of network nodes into communities, and modularity optimization is the most widely used class of methods for detecting communities in networks. In bipartite networks, there are correspondingly bipartite modularity and bipartite modularity optimization. LPAb, a very fast label propagation algorithm based on bipartite modularity optimization, tends to become stuck in poor local maxima, yielding suboptimal community divisions with low bipartite modularity. We therefore propose LPAb+, a hybrid algorithm combining modified LPAb, or LPAb', and MSG, a multistep greedy agglomerative algorithm, with the objective of using MSG to drive LPAb out of local maxima. We use four commonly used real-world bipartite networks to demonstrate LPAb+ capability in detecting community divisions with remarkably higher bipartite modularity than LPAb. We show how LPAb+ outperforms other bipartite modularity optimization algorithms, without compromising speed.