Fig. 4: Statistical properties of the rewired undirected network after optimizing synchronizability.

The distribution of the generalized nodes' degree Eq. (8) for networks with 2-hyperlink interactions under various sizes: a 6, b 10, c 20, d 50, e 80, f 100. The generalized nodes' degree distribution shows that the more synchronizable network tends to be homogeneous. Correspondingly, the homogeneity parameter^43,44,45,46g given by Eq. (16) is bigger for the rewired network, indicating more homogeneous nodes' degrees. The property of the more synchronizable 2-hyperlink interactions is consistent with 1-hyperlink interactions, where nodes also tend to be homogeneous in degree²⁶.