Community detection for directed networks revisited using bimodularity

2025-02-07

AI Summary

Conventional directed network community detection often neglects edge directionality, leading to structural distortion and biologically implausible partitions. Method: This paper introduces “bimodularity,” a novel criterion that models communities as coupled structures of sender- and receiver-oriented roles. We formally define a directed community as a synergistic mapping between these two role types and propose a bimodularity metric amenable to convex relaxation—ensuring both theoretical tractability and biological interpretability. The method integrates singular value decomposition of the directed modularity matrix, convex optimization relaxation, and edge-level clustering. Results: Evaluated on synthetic benchmarks and the *Caenorhabditis elegans* neuronal connectome, our approach successfully identifies feedforward circuitry in head and body motor systems, achieving significantly improved structural fidelity and consistency with known neurobiological organization.

Technology Category

• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Machine Learning: Bio-inspired Learning

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Web Mining and Content Analysis: Models for Web evolution

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 new 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 new framework is illustrated on a synthetic model and further applied to the neuronal wiring diagram of the extit{C. 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.

Problem

• Directed networks community detection
• Bimodularity for directed communities
• Edge-based clustering approach

Innovation

• Bimodularity optimizes directed community detection
• Convex relaxation with singular value decomposition
• Edge-based clustering reveals directed community mappings