Fig. 6: Nonpairwise interactions typically enhance synchronization in hypergraphs, except when they are close to being a simplicial complex.
This plot uses the same data as in Fig. 5 and explicitly shows the transition in how higher-order interactions affect synchronization as the hypergraph structure loses resemblance to simplicial complexes. Points in the upper-left half of the square represent hypergraphs for which higher-order interactions impede synchronization, while points in the lower-right half of the square represent hypergraphs for which higher-order interactions promote synchronization. As the shuffling probability ps is increased (ps = 0 corresponds to simplicial complexes), all six systems swiftly move across the diagonal line and into the synchronization-promoting region.
