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

<i>Objective.</i>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.<i>Approach.</i>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.<i>Main results.</i>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 onθandγbands. 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.<i>Significance.</i>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.