Effects of Hyperedge Overlap and Internal Structure on Hypernetwork Synchronization Dynamics

The internal structure of hyperedges has become central to understanding collective dynamics in hypernetworks. This study investigates the impact of hyperedge overlap on network synchronization when hyperedge structures are explicitly considered. We propose a modified hyper-adjacency matrix that captures the internal organization of the hyperedges while preserving the higher-order properties. Using this framework, we examine how non-complete connections within hyperedges influence synchronization as the overlap increases. Our findings reveal clear differences from fully connected hyperedge models. Furthermore, spectral graph theory and numerical simulations confirm that the structural variations induced by overlaps significantly regulate global synchronization. This work extends the theoretical framework of hypernetwork synchronization and highlights the critical role of hyperedge overlaps in shaping the internal hyperedge structure.