Optimal homogeneous networks with best possible synchronizability

A large number of real-world complex networks or their sub-networks possess excellent dynamical properties such as high dynamic synchronizability, optimal controllability, strong resistance to attacks, and fast information spreading capability, but existing network models are unable to well represent these intrinsic features and ubiquitous phenomena. This paper establishes an optimal homogeneous network model which can well describe at least one of such optimal dynamical behaviors — the best possible synchronizability.