Towards Pure High-Order Aggregation: Rethinking Multi-Hop Neighborhood Learning in Graph Convolutional Networks

Graph convolutional networks (GCNs) have achieved remarkable success in graph representation learning, yet they remain limited by over-smoothing and insufficient utilization of high-order topology. Existing high-order GCNs exploit multi-hop neighbors but ignore the purity of high-order neighborhoods: the high-order graphs they construct contain duplicated and fictional edges, which cause feature redundancy and false topological semantics. In this paper, we propose a pure high-order graph convolutional network (PHGCN) grounded in pure high-order neighborhoods. We first analyze how duplicated and fictional edges arise from powers of the adjacency matrix, and then design a graph pure high-order projection (GPHP) algorithm that eliminates both types of invalid edges. On this basis, we construct a multi-path GCN architecture with an attention-based fusion module to learn and combine features from pure high-order neighborhoods of different orders. Experiments on seven graph classification benchmarks (IMDB-B, IMDB-M, MUTAG, PROTEINS, NCI1, DD, and COLLAB) show that PHGCN achieves the best average ranking among the compared models, and ablation studies show that each component contributes to the final performance.