THE LOCALLY OPTIMAL STRUCTURE FOR SYNCHRONIZABILITY OF DYNAMICAL NETWORKS

Abstract

A network is referred to have locally optimal structure for synchronizability if its synchronizability is always decreased, no matter an arbitrary edge is added to it or an arbitrarily existed edge is deleted from it or an arbitrary edge is rewired in it. Although it is difficult to generally determine which networks have locally optimal structure, this paper through various examples demonstrates that symmetrical networks indeed have this property. Actually, it is found that any structural perturbations which destruct the symmetry of an originally symmetrical network would decrease the network's synchronizability, no matter how the perturbations change the network's average path length or clustering coefficient.