Detecting Communities in Complex Networks Using Formal Concept Analysis

The complex nature of many real-world networks is motivating researchers to investigate or extend network analysis methods such as centrality computation, link prediction, and community detection. One of these complex structures is the multilayer network in which each layer contains a network. Multilayer networks frequently possess complex local structures of multimodal data and interlinked relations. Thus, efficient detection of local communities in such networks often remains a key challenge. In this paper, we propose a community detection strategy, called CoDeBi, which leverages Formal Concept Analysis (FCA) to find possibly overlapping and nested communities in multilayer networks. At the preprocessing stage, we exploit operations such as apposition, subposition and composition on formal contexts—associated with individual layers—to generate a global formal context representing the whole multilayer network. At the first step of CoDeBi, we extract the formal concepts that capture groups in the global formal context while in the second step, we filter the extracted formal concepts to keep only the ones that have a high harmonic mean of stability and separation indices. Such groups represent core communities. In the third step, we detect final communities by refining the core groups using Silhouette Analysis. Our validation study shows that CoDeBi can accurately identify communities in bipartite graphs, and hence can be exploited for community detection in multilayer networks. Another contribution of this paper is the application of the attractive features of Triadic Concept Analysis and the adaptation of our approach to the analysis of tridimensional networks represented by a tridimensional adjacency matrix.