  We study the synchronization transition in scale-free networks that display
power-law asymptotic behaviors in their degree distributions. The critical
coupling strength and the order-parameter critical exponent derived by the mean
field approach depend on the degree exponent $\lambda$, which implies a close
connection between structural organization and the emergence of dynamical order
in complex systems. We also derive the finite-size scaling behavior of the
order parameter finding that the giant cluster of synchronized nodes is formed
in different ways between scale-free networks with $2<\lambda<3$ and those with
$\lambda>3$.
