Synchronizability is Enhanced in Homogeneous Small-world Networks

Using a rewiring-edge method without changing the degree distribution of a network, we propose a weighted homogeneous small-world (HOSW) network model in which all nodes have the same degree. It is found that with the increase of the rewiring probability, which is defined as the ratio of the number of rewiring edges to the total edges in the network, both the average clustering and average path length decrease, however, the network synchronizability is enhanced. Contrary to the result that the synchronizability of NW small-world network is enhanced with the increase of the network size [6], we find that for the same value of rewiring probability, the synchronizability of HOSW network is weakened with the increase of network size.