# Efficient Communication over Complex Dynamical Networks: The Role of Matrix Non-Normality

## TL;DR

This paper introduces a framework to analyze how network structure, noise, and interference affect information transmission in complex dynamical networks, highlighting the advantages of non-normal networks in noise cancellation and information throughput.

## Contribution

It develops a mathematical framework to understand information propagation in networks, revealing the benefits of non-normal structures over normal ones for communication efficiency.

## Key findings

- Non-normal networks can cancel noise effects by transiently amplifying input dimensions.
- Normal networks suffer from interference noise and are less efficient.
- Network wiring details often do not impact transmission quality in normal networks.

## Abstract

In both natural and engineered systems, communication often occurs dynamically over networks ranging from highly structured grids to largely disordered graphs. To use, or comprehend the use of, networks as efficient communication media requires understanding of how they propagate and transform information in the face of noise. Here, we develop a framework that enables us to examine how network structure, noise, and interference between consecutive packets jointly determine transmission performance in networks with linear dynamics at single nodes and arbitrary topologies. Mathematically normal networks, which can be decomposed into separate low-dimensional information channels, suffer greatly from readout and interference noise. Interestingly, most details of their wiring have no impact on transmission quality. Non-normal networks, however, can largely cancel the effect of noise by transiently amplifying select input dimensions while ignoring others, resulting in higher net information throughput. Our theory could inform the design of new communication networks, as well as the optimal use of existing ones.