2025-08-27 スイス連邦工科大学ローザンヌ校(EPFL)
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＜関連情報＞
- https://actu.epfl.ch/news/who-leads-and-who-follows-a-new-way-to-read-networ/
- https://www.pnas.org/doi/10.1073/pnas.2500571122
二モジュラリティを用いた有向ネットワークのコミュニティ検出再考 Community detection for directed networks revisited using bimodularity
Alexandre Cionca, Chun Hei Michael Chan, and Dimitri Van De Ville
Proceedings of the National Academy of Sciences Published:August 25, 2025
DOI:https://doi.org/10.1073/pnas.2500571122
Significance
The art of finding patterns or communities plays a central role in the analysis of structured data such as networks. Community detection in graphs has become a field on its own. Real-world networks, however, tend to describe asymmetric, directed relationships, and community detection methods have not yet reached consensus on how to define and retrieve communities in this setting. This work introduces a framework for the interpretation of directed graph partitions and communities, for which we define the bimodularity index and provide an optimization method to retrieve the embedding and detection of directed communities. The application of our approach to the worm neuronal wiring diagram highlights the importance of directed information that remains hidden from conventional community detection.
Abstract
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.
