  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.

Systems and Control;Optimization and Control;Adaptation and Self-Organizing Systems