Enhancing key node identification in hypernetworks: A novel node–hyperedge interaction model

Hypernetworks, as advanced structures in complex network analysis, are employed to model multifaceted relationships in intricate systems. Identifying key nodes in hypernetworks is crucial for enhancing network functionality and its overall robustness. However, existing methods often struggle to capture the complex interactions between nodes and hyperedges, leading to limited accuracy and monotonicity in identification. This study proposes a novel node–hyperedge interaction (NHI) model to address these challenges. NHI signifies the global hub role of nodes through node force on hyperedges and quantifies interaction strength between nodes and hyperedges using hyperedge influence, thereby improving the precision of discerning local and positional node attributes. Experimental results reveal that NHI effectively identifies nodes with strong spreading capabilities and significant influence on network structure. Meanwhile, NHI exhibits superior monotonicity in node differentiation and a stronger correlation with the Susceptible–Infected–Recovered (SIR) model, ensuring exceptional accuracy in key node identification.