Layered Complex Networks as Fluctuation Amplifiers

TL;DR

This paper studies how noise propagates and amplifies in multi-layer complex networks, revealing conditions that can lead to increased fluctuations and potential system vulnerabilities.

Contribution

It introduces an analytical framework to predict noise amplification in two-layer networks based on connectivity and eigenmode overlap.

Findings

Noise can be strongly amplified across layers depending on network connectivity.

Eigenmode overlap influences the extent of fluctuation amplification.

Analytical predictions are validated with numerical simulations on synthetic networks.

Abstract

In complex networked systems theory, an important question is how to evaluate the system robustness to external perturbations. With this task in mind, I investigate the propagation of noise in multi-layer networked systems. I find that, for a two layer network, noise originally injected in one layer can be strongly amplified in the other layer, depending on how well-connected are the complex networks in each layer and on how much the eigenmodes of their Laplacian matrices overlap. These results allow to predict potentially harmful conditions for the system and its sub-networks, where the level of fluctuations is important, and how to avoid them. The analytical results are illustrated numerically on various synthetic networks.