sHGCN: Simplified hyperbolic graph convolutional neural networks
To address the high computational cost and limited accuracy of hyperbolic graph neural networks (HGNNs) in modeling graphs on hyperbolic spaces, this paper proposes a Simplified Hyperbolic Graph Convolutional Network (S-HGCN). Methodologically, it introduces the first systematic simplification of core operations in the Poincaré ball model: lightweight hyperbolic exponential and logarithmic maps are designed, and the message propagation and aggregation mechanisms are reformulated to eliminate expensive geodesic distance computations. Crucially, these simplifications preserve low-distortion hyperbolic embeddings while substantially reducing time complexity. Extensive experiments demonstrate that S-HGCN achieves an average 2.3× speedup and a 1.8% improvement in accuracy across multiple graph learning benchmarks. By reconciling efficiency with expressiveness, S-HGCN establishes a new paradigm for scalable hyperbolic graph representation learning.