Average Range and Network Synchronizability

The influence of structural properties of a network on the network synchronizability is studied by introducing a new concept of average range of edges. For both small-world and scale-free networks, the effect of average range on the synchronizability of networks with bounded or unbounded synchronization regions is illustrated through numerical simulations. The relations between average range, range distribution, average distance, and maximum betweenness are also explored, revealing the effects of these factors on the network synchronizability of the small-world and scale-free networks, respectively.