Discovering Influential Nodes in Hypergraphs With MHRW Sampling and Isolating Centrality

Determining the influential nodes is a fundamental problem in analyzing the dynamics of a complex system. The complex systems are represented as hypergraphs, conventional centrality metrics, such as degree, closeness, betweenness and harmonic centralities have been extended from graph-based models to hypergraphs, but these adaptions fail to capture the unique structural characteristics and higher order relationships inherent in hypergraphs. To overcome these limitations, we proposed Isolating centrality (ISC), quantifies node influence by incorporating both local connectivity patterns and degree of structural isolation. To manage the computational complexity of analyzing large-scale hypergraphs, we employed the Metropolis-Hastings Random Walk (MHRW) sampling technique, traditionally used in graphs and extended to hypergraphs, by preserving the basic properties of hypergraphs. For this sampled hypergraph we computed ISC and compared it with traditional metrics by evaluation metrics such as SIR model, Kendall Tau correlation analysis.