  We consider complex clustered networks with a gradient structure, where sizes
of the clusters are distributed unevenly. Such networks describe more closely
actual networks in biophysical systems and in technological applications than
previous models. Theoretical analysis predicts that the network
synchronizability can be optimized by the strength of the gradient field but
only when the gradient field points from large to small clusters. A remarkable
finding is that, if the gradient field is sufficiently strong,
synchronizability of the network is mainly determined by the properties of the
subnetworks in the two largest clusters. These results are verified by
numerical eigenvalue analysis and by direct simulation of synchronization
dynamics on coupled-oscillator networks.
