FMHC: A Fuzzy Multi-Hierarchical Centrality Strategy for Node Evaluation in Hypergraphs

Accurately identifying influential nodes in complex networks is crucial for understanding their structure and dynamics. Traditional methods for measuring node centrality often struggle to capture the inherent uncertainties in node relationships and to model specific higher-order interaction patterns, limiting their reliable evaluations in hypergraph contexts. To address this challenge, we propose a novel approach called Fuzzy Multi-Hierarchical Centrality (FMHC), which integrates fuzzy theory with multi-hierarchical topological analysis for centrality assessment in hypergraphs. By synthesizing inter-node fuzzy distances, node-to-edge fuzzy membership degrees, and mutual information associations among nodes and edges, FMHC constructs a multi-hierarchical evaluation architecture to generate comprehensive and discriminative importance scores for each node. Extensive experiments on nine real-world datasets demonstrate that FMHC consistently outperforms eight classical and state-of-the-art benchmarks across three key evaluation criteria: the capacity to identify nodes with high spreading influence, alignment with the Susceptible-Infected-Recovered (SIR) epidemic model, and monotonicity in ranking discrimination. These findings validate the effectiveness, robustness, and superiority of FMHC in hypergraph environments.