Fig. 5: Synchronization stability of hypergraphs constructed from brain networks.
For each of the six brain networks, we start by attaching 2-simplices to closed triangles and turning the network into a simplicial complex. We then construct hypergraphs at different distances from the simplicial complex by randomly shuffling the 2-simplices with probability ps. For each value of ps, we plot synchronization stability λ2 as a function of the control parameter α (averaged over 50 independent realizations). It is clear that as the hypergraphs move further away from being a simplicial complex, synchronization stability is consistently improved. The role of higher-order interactions also generally transitions from impeding synchronization to promoting synchronization as ps is increased.
