Exponent-based hypergraph centrality for identifying vital nodes in higher-order brain networks

Higher-order brain interactions cannot be fully represented by ordinary pairwise graphs. Hypergraphs provide a natural framework for modeling multi-region interactions, but centrality measures for ranking clinically relevant nodes in higher-order brain networks remain incompletely evaluated.

We propose exponent-based hypergraph centrality (HEC), which transforms a hypergraph into a hyperedge adjacency graph and combines third Laplacian energy centrality with shortest-path distance in an exponential weighting model. Hyperedge scores are then mapped back to nodes. Patient-specific stereo-electroencephalography (SEEG) hypergraphs were constructed from thresholded phase-locking value (PLV) functional connectivity networks.

HEC was evaluated on real-world hypergraphs using complex contagion simulations and on SEEG-derived hypergraphs from 10 patients with refractory focal epilepsy. Across real-world datasets, HEC showed competitive and often leading spreading influence, although performance varied. In the SEEG cohort, HEC scores were higher in clinically defined epileptogenic zone (EZ) contacts than in non-epileptogenic zone (NEZ) contacts.

Compared with HDC, HCC, VC, HGC, and HVC, HEC produced the largest percentage contrast between EZ and NEZ contacts. Sensitivity analyses showed stable rankings and EZ/NEZ discrimination under perturbations of the distance-decay parameter and PLV threshold.

HEC provides a higher-order centrality measure for ranking vital nodes in hypergraphs and a quantitative tool for retrospective SEEG-based EZ-related network analysis. The results support offline feasibility at the studied SEEG scale, but prospective validation in larger cohorts is required before use in clinical decision-making.