  The understanding of synchronization ranging from natural to social systems
has driven the interests of scientists from different disciplines. Here, we
have investigated the synchronization dynamics of the Kuramoto dynamics
departing from the fully synchronized regime. We have got the analytic
expression of the dynamical correlation between pairs of oscillators that
reveals the relation between the network dynamics and the underlying topology.
Moreover, it also reveals the internal structure of networks that can be used
as a new algorithm to detect community structures. Further, we have proposed a
new measure about the synchronization in complex networks and scrutinize it in
small-world and scale-free networks. Our results indicate that the more
heterogeneous and "smaller" the network is, the more closely it would be
synchronized by the collective dynamics.
