Hierarchical Network Structure Promotes Dynamical Robustness

TL;DR

This paper investigates how hierarchical network structures enhance the robustness and stability of complex biological systems, revealing that modularity and hierarchy are key to dynamical resilience across various network types.

Contribution

It demonstrates that hierarchical modularity increases dynamical robustness and identifies permutation symmetry of modules as fundamental to system stability.

Findings

Robustness depends on links between modules.

Permutation of modules affects robustness.

Hierarchical structures maximize system stability.

Abstract

The relationship between network topology and system dynamics has significant implications for unifying our understanding of the interplay among metabolic, gene-regulatory, and ecosystem network architecures. Here we analyze the stability and robustness of a large class of dynamics on such networks. We determine the probability distribution of robustness as a function of network topology and show that robustness is classified by the number of links between modules of the network. We also demonstrate that permutation of these modules is a fundamental symmetry of dynamical robustness. Analysis of these findings leads to the conclusion that the most robust systems have the most hierarchical structure. This relationship provides a means by which evolutionary selection for a purely dynamical phenomenon may shape network architectures across scales of the biological hierarchy.