Community detection has been extensively studied for various applications, focusing primarily on network topologies. Recent research has started to explore node contents to identify semantically meaningful communities and interpret their structures using selected words. However, links in real networks typically have semantic descriptions, e.g., comments and emails in social media, supporting the notion of communities of links. Indeed, communities of links can better describe multiple roles that nodes may play and provide a richer characterization of community behaviors than communities of nodes. The second issue in community finding is that most existing methods assume network topologies and descriptive contents to be consistent and to carry the compatible information of node group membership, which is generally violated in real networks. These methods are also restricted to interpret one community with one topic. The third problem is that the existing methods have used top ranked words or phrases to label topics when interpreting communities. However, it is often difficult to comprehend the derived topics using words or phrases, which may be irrelevant. To address these issues altogether, we propose a new unified probabilistic model that can be learned by a dual nested expectation-maximization algorithm. Our new method explores the intrinsic correlation between communities and topics to discover link communities robustly and extract adequate community summaries in sentences instead of words for topic labeling at the same time. It is able to derive more than one topical summary per community to provide rich explanations. We present experimental results to show the effectiveness of our new approach, and evaluate the quality of the results by a case study.

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.