  The contradiction between the fact that many empirical networks possess
power-law degree distribution and the finding that network of heterogeneous
degree distribution is difficult to synchronize has been a paradox in the study
of network synchronization. Surprisingly, we find that this paradox can be well
fixed when proper gradients are introduced to the network links, i.e.
heterogeneity is in favor of synchronization in gradient networks. We analyze
the statistical properties of gradient networks and explore their dependence to
the other network parameters. Based on these understandings, we further propose
a new scheme for network synchronization distinguished by using less network
information while reaching stronger synchronizability, as supported by
analytical estimates of eigenvalues and directed simulations of coupled chaotic
oscillators. Our findings suggest that, with gradient, scale-free network is a
natural choice for synchronization.
