Structure-and-embedding-based centrality on network fragility in hypergraphs

Revealing the critical nodes is crucial to maintain network safety. Various methods have been proposed to identify the vital nodes and, recently, have been generalized from ordinary networks to hypergraphs. However, many existing methods did not consider both the hypergraph structure and embedding. In this article, we investigate two topological structural centralities by considering the common nodes and the common hyperedges and a hypergraph embedding centrality based on representation learning. Four improved centralities are proposed by considering only the node embedding, and the joint of the node embedding and hypergraph structural common nature. The network fragility is investigated for six real datasets. The proposed methods are found to outperform the baseline methods in five hypergraphs, and incorporating the embedding feature into the structural centralities can greatly improve the performance of the single structure-based centralities. The obtained results are heuristically understood by a similarity analysis of the node embeddings.