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
, 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
... [Show full abstract] 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.