Synchronizability of network ensembles with prescribed statistical properties

It has been shown that synchronizability of a network is determined by the local structure rather than the global properties. With the same global properties, networks may have very different synchronizability. In this paper, we numerically studied, through the spectral properties, the synchronizability of ensembles of networks with prescribed statistical properties. Given a degree sequence, it is found that the eigenvalues and eigenratios characterizing network synchronizability have well-defined distributions, and statistically, the networks with extremely poor synchronizability are rare. Moreover, we compared the synchronizability of three network ensembles that have the same nodes and average degree. Our work reveals that the synchronizability of a network can be significantly affected by the local pattern of connections, and the homogeneity of degree can greatly enhance network synchronizability for networks of a random nature.