Relations between average distance, heterogeneity and network synchronizability

By using the random interchanging algorithm, we investigate the relations between average distance, standard deviation of degree distribution and synchronizability of complex networks. We find that both increasing the average distance and magnifying the degree deviation will make the network synchronize harder. Only the combination of short average distance and small standard deviation of degree distribution ensures strong synchronizability. Some previous studies assert that the maximal betweenness is the right quantity to estimate network synchronizability: the larger the maximal betweenness, the poorer the network synchronizability. Here we address an interesting case, which strongly suggests that the single quantity, maximal betweenness, may not give a comprehensive description of network synchronizability.