Fig. 1: Synchronization is enhanced by higher-order interactions in random hypergraphs but is impeded in simplicial complexes.

The maximum transverse Lyapunov exponent λ2 is plotted against α for random hypergraphs (blue) and simplicial complexes (green). As α is increased, the coupling goes from first-order-only (α = 0) to second-order-only (α = 1). Each point represents the average over 50 independent hypergraphs or simplicial complexes with n = 100 nodes. The error bars represent standard deviations. We set p = p△ = 0.1 for random hypergraphs and p = 0.5 for simplicial complexes.