Lower Ricci Curvature for Hypergraphs

• URL: http://arxiv.org/abs/2506.03943v1
• Date: Wed, 04 Jun 2025 13:32:09 GMT
• Title: Lower Ricci Curvature for Hypergraphs
• Authors: Shiyi Yang, Can Chen, Didong Li,
• Abstract summary: We introduce hypergraph lower curvature (HLRC), a novel curvature metric defined in closed form that achieves a principled balance between interpretability and efficiency.<n>HLRC consistently reveals meaningful higher-order organization, distinguishing intra-community hyperedges, uncovering latent semantic labels, tracking temporal dynamics, and supporting robust clustering of hypergraphs based on global structure.
• Score: 3.9965784551765697
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Networks with higher-order interactions, prevalent in biological, social, and information systems, are naturally represented as hypergraphs, yet their structural complexity poses fundamental challenges for geometric characterization. While curvature-based methods offer powerful insights in graph analysis, existing extensions to hypergraphs suffer from critical trade-offs: combinatorial approaches such as Forman-Ricci curvature capture only coarse features, whereas geometric methods like Ollivier-Ricci curvature offer richer expressivity but demand costly optimal transport computations. To address these challenges, we introduce hypergraph lower Ricci curvature (HLRC), a novel curvature metric defined in closed form that achieves a principled balance between interpretability and efficiency. Evaluated across diverse synthetic and real-world hypergraph datasets, HLRC consistently reveals meaningful higher-order organization, distinguishing intra- from inter-community hyperedges, uncovering latent semantic labels, tracking temporal dynamics, and supporting robust clustering of hypergraphs based on global structure. By unifying geometric sensitivity with algorithmic simplicity, HLRC provides a versatile foundation for hypergraph analytics, with broad implications for tasks including node classification, anomaly detection, and generative modeling in complex systems.

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