title: The diminishing role of hubs in dynamical processes on complex networks.
abstract: It is notoriously difficult to predict the behaviour of a complex self-organizing system, where the interactions among dynamical units form a heterogeneous topology. Even if the dynamics of each microscopic unit is known, a real understanding of their contributions to the macroscopic system behaviour is still lacking. Here, we develop information-theoretical methods to distinguish the contribution of each individual unit to the collective out-of-equilibrium dynamics. We show that for a system of units connected by a network of interaction potentials with an arbitrary degree distribution, highly connected units have less impact on the system dynamics when compared with intermediately connected units. In an equilibrium setting, the hubs are often found to dictate the long-term behaviour. However, we find both analytically and experimentally that the instantaneous states of these units have a short-lasting effect on the state trajectory of the entire system. We present qualitative evidence of this phenomenon from empirical findings about a social network of product recommendations, a protein-protein interaction network and a neural network, suggesting that it might indeed be a widespread property in nature.
authors.affiliation: Computational Science, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands. r.quax@uva.nl
authors.forename: Rick
authors.initials: R
authors.lastname: Quax
authors.forename: Andrea
authors.initials: A
authors.lastname: Apolloni
authors.forename: Peter M A
authors.initials: PM
authors.lastname: Sloot
mesh_terms: D008954:Models, Biological; D016571:Neural Networks, Computer
keywords: complex networks; gene regulatory networks; information theory; neural networks; out-of-equilibrium dynamics; word-of-mouth marketing