  We investigate collective synchronization in a system of coupled oscillators
on small-world networks. The order parameters which measure synchronization of
phases and frequencies are introduced and analyzed by means of dynamic
simulations and finite-size scaling. Phase synchronization is observed to
emerge in the presence of even a tiny fraction $P$ of shortcuts and to display
saturated behavior for $P \gtrsim 0.5$. This indicates that the same
synchronizability as the random network (P=1) can be achieved with relatively
small number of shortcuts. The transient behavior of the synchronization,
obtained from the measurement of the relaxation time, is also discussed.
