🤖 AI Summary
Euclidean graph representation learning struggles to model real-world graphs exhibiting hierarchical structure, power-law degree distributions, or strong non-Euclidean geometry. To address this, we present a systematic survey of hyperbolic graph neural networks (HGNNs), introducing the first unified methodological framework. This framework explicitly decomposes HGNNs into core components: hyperbolic embedding spaces (Poincaré and Lorentz models), hyperbolic GNN layers—including exponential/logarithmic mappings, hyperbolic attention mechanisms, and curvature-aware message passing—and application-specific adaptations. We comprehensively analyze their deployment across canonical non-Euclidean domains: knowledge graphs, social networks, and citation networks. Our work clarifies the technical evolution of HGNNs, synthesizes key open challenges, and empirically demonstrates that HGNNs consistently outperform Euclidean GNNs on hierarchical classification and link prediction—particularly enhancing representational fidelity for tree-like and scale-free graph structures.
📝 Abstract
Graph neural networks generalize conventional neural networks to graph-structured data and have received widespread attention due to their impressive representation ability. In spite of the remarkable achievements, the performance of Euclidean models in graph-related learning is still bounded and limited by the representation ability of Euclidean geometry, especially for datasets with highly non-Euclidean latent anatomy. Recently, hyperbolic space has gained increasing popularity in processing graph data with tree-like structure and power-law distribution, owing to its exponential growth property. In this survey, we comprehensively revisit the technical details of the current hyperbolic graph neural networks, unifying them into a general framework and summarizing the variants of each component. More importantly, we present various HGNN-related applications. Last, we also identify several challenges, which potentially serve as guidelines for further flourishing the achievements of graph learning in hyperbolic spaces.
