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Community detection of undirected hypergraphs by Ricci flow
Yulu Tian1, Jicheng Ma2, Yunyan Yang2
1Beijing Normal University, School of Mathematical Sciences, Key Laboratory of Mathematics and Complex Systems of MOE, Beijing 100875, China.
Physical Review. E
|November 18, 2025
Summary
We introduce HyperRCD, a novel method for community detection in hypergraphs. This approach utilizes hypergraph Ricci flow to effectively identify functional modules by analyzing higher-order interactions, showing robust performance across datasets.
Area of Science:
- Graph theory
- Network science
- Computational mathematics
Background:
- Community detection is crucial for understanding complex systems.
- Hypergraphs capture higher-order interactions, but analyzing them is challenging.
- Existing methods struggle with the complexity of hypergraph structures.
Purpose of the Study:
- To develop a robust community detection method for hypergraphs.
- To leverage hypergraph Ricci flow for analyzing higher-order interactions.
- To enhance the identification of functional modules in complex networks.
Main Methods:
- Defined a hypergraph Ricci flow applicable to undirected hypergraphs.
- Proved the long-time existence of the hypergraph Ricci flow.
- Developed HyperRCD, a Ricci-flow-based algorithm deforming hyperedge weights via curvature-driven evolution.
Main Results:
- HyperRCD effectively represents higher-order interactions through weighted hyperedges.
- Demonstrated enhanced robustness to topological variations in experiments.
- Achieved competitive performance on both synthetic and real-world hypergraph datasets.
Conclusions:
- HyperRCD offers a powerful new tool for hypergraph community detection.
- The hypergraph Ricci flow provides a solid theoretical basis for network analysis.
- This method advances the study of functional modules in complex systems.
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