On synchronizability and heterogeneity in unweighted networks

Synchronization in classes of continuous-time dynamical unweighted networks with different topologies is investigated. A synchronization-optimal network model based on rewiring of links is proposed. Compared with other networks, it exhibits a stronger synchronizability. We presented link density and investigated the correlation of synchronizability, link density and heterogeneity in degree distribution. In this work, it will be shown that synchronizability of Type I networks is independent of heterogeneity in the degree distribution when the link density is smaller than 0.02. Synchronizability and link density are proportional. When the link density is larger than 0.025, heterogeneity decides the curve slope. The synchronizability of Type II networks is drastically enhanced by enhancing the link density when the link density is smaller than 0.025. However synchronizability increases weakly by enhancing the link density when the link density is larger than 0.025.