Algorithm for Identifying Critical Nodes in Networks Based on Spectral Clustering to Construct Hypergraphs

Currently, the basis for critical nodes definition and identification lies in the representation learning of the network and the extraction of local and global features of the nodes. The effectiveness of the algorithm is closely related to network modeling and network structural characteristics. However, with the increasing complexity of real-world systems, utilizing the continuity and integrity of traditional bipartite graph representation faces significant challenges. Different from traditional graph modeling, the hyperedges of a hypergraph can connect multiple nodes simultaneously, thus forming richer structural features and interaction information between nodes for the analysis and judgment of critical nodes. To more accurately identify critical nodes in complex networks, we propose an algorithm that establishes a hypergraph representation for traditional graph data to extract higher-order features of nodes for neural network training, in order to identify critical nodes in complex networks. The effectiveness of this method is proven by comparing it with various critical node identification algorithms under different infection rates.