Synchronization between two coupled complex networks

We study synchronization for two unidirectionally coupled networks. This is a substantial generalization of several recent papers investigating synchronization inside a network. We derive analytically a criterion for the synchronization of two networks which have the same (inside) topological connectivity. Then numerical examples are given which fit the theoretical analysis. In addition, numerical calculations for two networks with different topological connections are presented and interesting synchronization and desynchronization alternately appear with increasing value of the coupling strength.