  Using a recently described technique for manipulating the clustering
coefficient of a network without changing its degree distribution, we examine
the effect of clustering on the synchronization of phase oscillators on
networks with Poisson and scale-free degree distributions. For both types of
network, increased clustering hinders global synchronization as the network
splits into dynamical clusters that oscillate at different frequencies.
Surprisingly, in scale-free networks, clustering promotes the synchronization
of the most connected nodes (hubs) even though it inhibits global
synchronization. As a result, scale-free networks show an additional, advanced
transition instead of a single synchronization threshold. This cluster-enhanced
synchronization of hubs may be relevant to the brain with its scale-free and
highly clustered structure.
