Characterizing Higher-order Functional Brain Networks with Simplicial Complexes and Temporal Dynamics.

While conventional approaches characterize brain functional connectivity using static, pairwise interactions, higher-order interactions among multiple regions and their temporal organization are also essential for understanding complex brain dynamics. Here, we propose a temporal higher-order functional brain network framework (THFBN) that integrates simplicial complexes with temporal dynamical modeling to infer directed, time-varying higher-order interactions from stereoelectroencephalography (SEEG) recordings in epilepsy. We show that higher-order interactions across time reveals structured network reconfigurations that are not captured by static higher-order representations alone, giving rise to rapid yet structured network reconfigurations that are not captured by static or pairwise representations. Applying THFBN to epileptic seizures reveals a spatially heterogeneous redistribution of higher-order positive and negative predictive influences across seizure stages, with the strongest variability observed in temporal and insular regions, while positive-negative balance remains generally stable despite substantial changes in influence strength. Together, these findings demonstrate that integrating temporal dynamics with higher-order interactions reveals structured network reconfigurations during seizure evolution that are not captured by conventional connectivity models, and provide a principled framework for studying dynamic higher-order brain organization in epilepsy.