  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 that ensures strong synchronizability. Some
previous studies assert that the maximal betweenness is a 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.
