Synchronization optimal networks obtained using local structure information

In this paper, the networks with optimal synchronizability are obtained using the local structure information. In scale-free networks, a node will be coupled by its neighbors with maximal degree among the neighbors if and only if the maximal degree is larger than its own degree. If the obtained coupled networks are connected, they are synchronization optimal networks. The connection probability of coupled networks is greatly affected by the average degree which usually increases with the average degree. This method could be further generalized by taking into account the degree of next-nearest neighbors, which will sharply increase the connection probability. Compared to the other proposed methods that obtain synchronization optimal networks, our method uses only local structure information and can hold the structure properties of the original scale-free networks to some extent. Our method may present a useful way to manipulate the synchronizability of real-world scale-free networks.