Discovery of communities in networks is a fundamental data analysis problem. Most of the existing approaches have focused on discovering communities of nodes, while recent studies have shown great advantages and utilities of the knowledge of communities of links. Stochastic models provides a promising class of techniques for the identification of modular structures, but most stochastic models mainly focus on the detection of node communities rather than link communities. We propose a stochastic model, which not only describes the structure of link communities, but also considers the heterogeneous distribution of community sizes, a property which is often ignored by other models. We then learn the model parameters using a method of maximum likelihood based on an expectation-maximization algorithm. To deal with large complex real networks, we extend the method by a strategy of iterative bipartition. The extended method is not only efficient, but is also able to determine the number of communities for a given network. We test our approach on both synthetic benchmarks and real-world networks including an application to a large biological network, and also compare it with two existing methods. The results demonstrate the superior performance of our approach over the competing methods for detecting link communities.

An important problem in analyzing complex networks is discovery of modular or community structures embedded in the networks. Although being promising for identifying network communities, the popular stochastic models often do not preserve node degrees, thus reducing their representation power and applicability to real-world networks. Here we address this critical problem. Instead of using a blockmodel, we adopted a random-graph null model to faithfully capture community structures by preserving in the model the expected node degrees. The new model, learned using nonnegative matrix factorization, is more accurate and robust in representing community structures than the existing methods. Our results from extensive experiments on synthetic benchmarks and real-world networks show the superior performance of the new method over the existing methods in detecting both disjoint and overlapping communities.