Optimizing higher-order network topology for synchronization of coupled phase oscillators

Networks in nature have complex interactions among agents. One significant phenomenon induced by interactions is synchronization of coupled agents, and the interactive network topology can be tuned to optimize synchronization. Previous studies showed that the optimized conventional network with pairwise interactions favors a homogeneous degree distribution of nodes for undirected interactions, and is always structurally asymmetric for directed interactions. However, the optimal control on synchronization for prevailing higher-order interactions is less explored. Here, by considering the higher-order interactions in a hypergraph and the Kuramoto model with 2-hyperlink interactions, we find that the network topology with optimized synchronizability may have distinct properties. For undirected interactions, optimized networks with 2-hyperlink interactions by simulated annealing tend to become homogeneous in the nodes’ generalized degree. We further rigorously demonstrate that for directed interactions, the structural symmetry can be preserved in the optimally synchronizable network with 2-hyperlink interactions. The results suggest that controlling the network topology of higher-order interactions leads to synchronization phenomena beyond pairwise interactions.