Modular organisation of interaction networks based on asymptotic dynamics

TL;DR

This paper presents a theoretical framework for analyzing modularity in biological interaction networks based on their asymptotic dynamics, revealing conditions for modular organization and finer decompositions.

Contribution

It introduces formal conditions for modularity in interaction networks and shows that strongly connected components form a natural modular decomposition.

Findings

Strongly connected components satisfy modularity conditions

Framework allows finer decomposition into elementary modules

Provides formal criteria for modular organization

Abstract

This paper investigates questions related to the modularity in discrete models of biological interaction networks. We develop a theoretical framework based on the analysis of their asymptotic dynamics. More precisely, we exhibit formal conditions under which agents of interaction networks can be grouped into modules. As a main result, we show that the usual decomposition in strongly connected components fulfils the conditions of being a modular organisation. Furthermore, we point out that our framework enables a finer analysis providing a decomposition in elementary modules.