# On Synchronization of Interdependent Networks

arXiv: https://arxiv.org/abs/1304.4731 · HTML: https://mlsanity.com/paper/1304.4731/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Apr 2013.

## Built on by (most cited first, 1 of 1)

- [A Tensor-Based Formulation of Hetero-functional Graph Theory](https://mlsanity.com/paper/2101.07220/) (2021)

## Abstract (arXiv)

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 μN-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.