Evaluating group interactions in epileptic brain networks by hypergraph and higher-order homophily

Abstract Objective. Group interactions capture cooperative dynamics among neural populations quantitatively, while also enabling precise detection of ensemble-level synchrony patterns and transcending the limitations of node-level relationships. To evaluate higher-order group interactions, we propose the PLASSO-homophily framework using multichannel stereo-electroencephalography (SEEG) recorded from patients with epilepsy. Approach. Specifically, we use phase locking value to improve least absolute shrinkage and selection operator method for constructing hypergraphs. Afterwards, we calculate affinity ratios between brain zones. Finally, we investigate higher-order interactions among different groups from a homophily perspective. The extremal result of strict homophily serves as a crucial theoretical framework for understanding homophily concepts, reflecting the constraints that different groups follow in higher-order interactions. Main results. It is observed that group interactions between seizure onset zones (SOZ), propagation zones (PZ) and non-involved zones (NIZ) present significant distinction across different seizure phases. In particular, the homophily of SOZ reaches a peak point during the seizure and sharply decreases in the post-seizure, with the most statistically significant differences on θ and γ bands. Furthermore, during the seizure, SOZ-PZ exhibits enhanced coupling while SOZ-NIZ exhibits impaired functional integration. Finally, among three groups, only SOZ exhibits strict monotonic and majority homophily. Significance. By analyzing changes in in-class and out-class connectivity, we quantitatively assess the activity levels and combinatorial constraints of the SOZ, PZ, and NIZ, thereby providing a novel perspective for exploring seizure mechanisms and developing epilepsy treatments.