# Spectral properties of the Laplacian of multiplex networks

arXiv: https://arxiv.org/abs/1307.2090 · HTML: https://mlsanity.com/paper/1307.2090/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jul 2013.

## Built on by (most cited first, 7 of 7)

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- [A tutorial on the dynamic Laplacian](https://mlsanity.com/paper/2408.04149/) (2024)

## Abstract (arXiv)

One of the more challenging tasks in the understanding of dynamical properties of models on top of complex networks is to capture the precise role of multiplex topologies. In a recent paper, Gomez et al. [Phys. Rev. Lett. 101, 028701 (2013)] proposed a framework for the study of diffusion processes in such networks. Here, we extend the previous framework to deal with general configurations in several layers of networks, and analyze the behavior of the spectrum of the Laplacian of the full multiplex. We derive an interesting decoupling of the problem that allow us to unravel the role played by the interconnections of the multiplex in the dynamical processes on top of them. Capitalizing on this decoupling we perform an asymptotic analysis that allow us to derive analytical expressions for the full spectrum of eigenvalues. This spectrum is used to gain insight into physical phenomena on top of multiplex, specifically, diffusion processes and synchronizability.