  While shorter characteristic path length has in general been believed to
enhance synchronizability of a coupled oscillator system on a complex
network,the suppressing tendency of the heterogeneity of the degree
distribution, even for shorter characteristic path length, has also been
reported. To see this, we investigate the effects of various factors such as
the degree, characteristic path length, heterogeneity, and betweenness
centrality on synchronization, and find a consistent trend between the
synchronization and the betweenness centrality. The betweenness centrality is
thus proposed as a good indicator for synchronizability.
