K-hop Hypergraph Neural Network: A Comprehensive Aggregation Approach

Abstract The powerful capability of HyperGraph Neural Networks (HGNNs) in modeling intricate, high-order relationships among multiple data samples stems primarily from their ability to aggregate both the direct neighborhood features of individual nodes and those associated with hyperedges. However, the limited scope of feature propagation in existing HGNNs significantly reduces the utilization of hypergraph information, exacerbating over-squashing and over-smoothing issues. To this end, we propose a novel K-hop HyperGraph Neural Network (KHGNN) to facilitate the interactions of distant nodes and hyperedges. Specifically, the bisection nested convolution based on HyperGINE is employed to extract features from nodes, hyperedges, and structures along all shortest paths between nodes or hyperedges, providing representations of long-distance relationships. With these comprehensive path features, nodes and hyperedges are guided to aggregate distant information while learning their complex relationships. The extensive experiments, particularly on long-range graph datasets, demonstrate that the proposed method achieves SOTA performance compared to existing HGNNs and graph neural networks.