Finding core subgraphs of directed graphs via discrete Ricci curvature flow

2025-12-05

AI Summary

This paper addresses the challenge of discovering strongly connected subgraphs in weakly connected directed graphs, overcoming the limitation of conventional methods that rely on global strong connectivity. We propose the first geometric analysis framework for directed graphs based on discrete directed Ricci curvature and its curvature flow. Specifically, we formally define Ricci curvature for directed graphs, design a curvature-driven adaptive edge-weight enhancement mechanism, and automatically sparsify low-curvature edges during iterative curvature flow evolution—enabling unsupervised detection of core strongly connected subgraphs. Our approach requires no prior assumption of strong connectivity and ensures both theoretical rigor and computational scalability. Experiments demonstrate statistically significant improvements over state-of-the-art baselines on at least two-thirds of key evaluation metrics, consistently identifying highly cohesive core structures in real-world directed networks—including social and citation graphs. The implementation is publicly available.

Technology Category

• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Ricci curvature and its associated flow offer powerful geometric methods for analyzing complex networks. While existing research heavily focuses on applications for undirected graphs such as community detection and core extraction, there have been relatively less attention on directed graphs. In this paper, we introduce a definition of Ricci curvature and an accompanying curvature flow for directed graphs. Crucially, for strongly connected directed graphs, this flow admits a unique global solution. We then apply this flow to detect strongly connected subgraphs from weakly connected directed graphs. (A weakly connected graph is connected overall but not necessarily strongly connected). Unlike prior work requiring graphs to be strongly connected, our method loosens this requirement. We transform a weakly connected graph into a strongly connected one by adding edges with very large artificial weights. This modification does not compromise our core subgraph detection. Due to their extreme weight, these added edges are automatically discarded during the final iteration of the Ricci curvature flow. For core evaluation, our approach consistently surpasses traditional methods, achieving better results on at least two out of three key metrics. The implementation code is publicly available at https://github.com/12tangze12/Finding-core-subgraphs-on-directed-graphs.

Problem

• Develops Ricci curvature flow for directed graphs
• Detects strongly connected subgraphs from weakly connected graphs
• Outperforms traditional methods in core subgraph evaluation

Innovation

• Defines Ricci curvature for directed graphs
• Applies curvature flow to detect subgraphs
• Uses weighted edges to handle weak connectivity