Community detection for directed networks revisited using bimodularity

• 成果类型: Article
• 署名作者: Cionca, Alexandre; Chan, Chun Hei Michael; Van De Ville, Dimitrivan
• 署名单位: Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; University of Geneva
• 刊物名称: PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
• ISSN/ISSBN: 0027-9167
• DOI: 10.1073/pnas.2500571122
• 发表日期: 2025-09-02
• 关键词: stochastic blockmodels; graphs

摘要

Community structure is a key feature omnipresent in real-world network data. Plethora of methods have been proposed to reveal subsets of densely interconnected nodes using criteria such as the modularity index. These approaches have been successful for undirected graphs but directed edge information has not yet been dealt with in a satisfactory way. Here, we revisit the concept of directed communities as a mapping between sending and receiving communities. This translates into a definition that we term bimodularity. Using convex relaxation, bimodularity can be optimized with the singular value decomposition of the directed modularity matrix. Subsequently, we propose an edge-based clustering approach to reveal the directed communities including their mappings. The feasibility of the framework is illustrated on a synthetic model and further applied to the neuronal wiring diagram of the Caenorhabditis elegans, for which it yields meaningful feedforward loops of the head and body motion systems. This framework sets the ground for the understanding and detection of community structures in directed networks.