Analysis of modular organisation of interaction networks based on asymptotic dynamics

Abstract : This paper investigates questions related to modularity in biological interaction networks. We develop a discrete theoretical framework based on the analysis of the asymptotic dynamics of biological interaction networks. More precisely, we exhibit formal conditions under which agents of interaction networks can be grouped into modules, forming a modular organisation. Our main result is that the conventional decomposition into strongly connected components fulfills the formal conditions of being a modular organisation. We also propose a modular and incremental algorithm for an efficient equilibria computation. Furthermore, we point out that our framework enables a finer analysis providing a decomposition in elementary modules, possibly smaller than strongly connected components.