Investigating Hypernode Classification of Complex Systems Based on High-order Graph Neural Networks

Investigating latent interactions beyond direct connections is essential for analyzing complex networks. However, traditional graph structures often fail to capture complex relationships, especially in the high-order interactions among multiple individuals. To address this issue, we extend the graph isomorphism network (GIN) framework to hypergraphs, treat nodes as self-hyperedges, and propose the self-hypergraph isomorphism network (SHGIN). Meanwhile, the hypergraph Weisfeiler–Lehman (WL) test is also proposed to distinguish different isomorphisms of hypergraphs and improve the representation power of hypergraph neural networks. Extensive experiments on co-authorship and co-citation networks demonstrate the effectiveness of SHGIN. The results indicate that our model displays superior hypernode classification accuracy compared to traditional graph neural networks in semi-supervised learning (SSL). Furthermore, it surpasses existing hypergraph neural network models in co-authorship datasets, highlighting its effectiveness in capturing high-order relationships in complex networks.