Evaluation of human epileptic brain networks by constructing simplicial complexes

As a powerful framework, higher-order networks have gained significant attention to model the non-pairwise interactions of complex systems. Particularly, simplicial complex is an important mathematical tool which can be used to depict higher-order interactions. However, previous works on simplicial complexes have mainly focused on synthetic data. In this paper, we propose a method based on multivariate phase synchronization to construct simplicial complexes using multichannel stereo-electroencephalography (SEEG) data recorded from epilepsy patients. Furthermore, we examine its ability to describe both global and local characteristics of the higher-order brain network. Specifically, we first introduce the Hodge Laplacian to characterize higher-order interactions and employ the Euler characteristic number to determine the network synchronizability which is a significant global characteristic. Afterwards, we define an improved gravity-based centrality method to identify vital nodes in the higher-order network with simplicial complexes. Additionally, network efficiency based on the higher-order distance between different nodes is adopted to evaluate the effectiveness of this method in distinguishing the important nodes. In particular, we find that the Hippocampus and Fusiform gyrus may promote the synchronization of the epileptic brain network. All in all, we believe that our method paves the way to investigate brain networks with higher-order interactions, which contributes to identifying hubs in the epileptic network and has potential applications in epileptic treatment.