  In the past decade, synchronization on complex networks has attracted
increasing attentions from various research disciplines. Most previous works,
however, focus only on the dynamic behaviors of synchronization process in the
stable region, i.e., global synchronization. In this letter, we demonstrate
that synchronization process on complex networks can efficiently reveal the
substructures of networks when the coupling strength of chaotic oscillators is
under the lower boundary of stable region. Both analytic and numerical results
show that the nodes belonging to the same component in the hierarchical network
are tightly clustered according to the Euclidean distances between the state
vectors of the corresponding oscillators, and different levels of hierarchy can
be systematically unfolded by gradually tuning the coupling strength. When the
coupling strengths exceed the upper boundary of stable region, the hierarchy of
the network cannot be recognized by this approach. Extensive simulations
suggest that our method may provide a powerful tool to detect the hierarchical
community structure of complex systems and deep insight into the relationship
between structure and dynamics of complex systems.
