Cionca Alexandre, Chan Chun Hei Michael, Van De Ville Dimitri
Neuro-X Institute, École Polytechnique Fédérale de Lausanne, Geneva 1202, Switzerland.
Department of Radiology and Medical Informatics, University of Geneva, Geneva 1202, Switzerland.
Proc Natl Acad Sci U S A. 2025 Sep 2;122(35):e2500571122. doi: 10.1073/pnas.2500571122. Epub 2025 Aug 25.
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 , 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.
社区结构是现实世界网络数据中普遍存在的一个关键特征。人们已经提出了大量方法，以使用诸如模块度指数等标准来揭示紧密相连节点的子集。这些方法在无向图方面取得了成功，但有向边信息尚未得到令人满意的处理。在这里，我们重新审视有向社区的概念，将其作为发送社区和接收社区之间的一种映射。这转化为一个我们称之为双模块度的定义。通过凸松弛，双模块度可以用有向模块度矩阵的奇异值分解来优化。随后，我们提出一种基于边的聚类方法来揭示有向社区及其映射。该框架的可行性在一个合成模型上得到了说明，并进一步应用于[具体对象]的神经元接线图，由此产生了头部和身体运动系统有意义的前馈回路。该框架为理解和检测有向网络中的社区结构奠定了基础。
