Abstract
Hypergraphs capture groupwise relationships among multiple nodes and often exhibit tree-like structures. Although hyperbolic space is well suited for modeling such structures, simply extending existing hypergraph representation learning (HRL) methods to hyperbolic space does not consistently improve performance. In this paper, we investigate the relationship between node structural properties and hyperbolic embedding radii and find that bridge nodes tend to lie closer to the center in graphs, whereas this relationship is not consistently observed in hypergraphs. We further find that conventional bridge score estimation may fail to capture the groupwise connectivity of hypergraphs. Motivated by these findings, we propose HyBridge, a self-supervised hyperbolic HRL framework that (1) estimates node bridge scores by considering the external connectivity of individual hyperedges, (2) learns node and hyperedge embeddings through hyperbolic hypergraph encoding, (3) guides node radial positions according to their bridge scores, and (4) employs contrastive learning to preserve node discriminability. Extensive experiments on 10 real-world hypergraphs demonstrate that HyBridge outperforms 22 competing methods, achieving performance improvements of up to 9.82% in node classification. For reproducibility, we provide the code at this https URL.
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URL
https://arxiv.org/abs/2611.16351
