On Synchronization of Interdependent Networks

It is well-known that the synchronization of diffusively-coupled systems on networks strongly depends on the network topology. In particular, the so-called algebraic connectivity $\mu_{N-1}$, or the smallest non-zero eigenvalue of the discrete Laplacian operator plays a crucial role on synchronization, graph partitioning, and network robustness. In our study, synchronization is placed in the general context of networks-of-networks, where single network models are replaced by a more realistic hierarchy of interdependent networks. The present work shows, analytically and numerically, how the algebraic connectivity experiences sharp transitions after the addition of sufficient links among interdependent networks.