ARTICLES Self-organized network evolution coupled to extremal dynamics

The interplay between topology and dynamics in complex networks is a fundamental but widely unexplored problem. Here, we study this phenomenon on a prototype model in which the network is shaped by a dynamical variable. We couple the dynamics of the Bak– Sneppen evolutionmodel with the rules of the so-called fitness networkmodel for establishing the topology of a network; each vertex is assigned a ‘fitness’, and the vertex with minimum fitness and its neighbours are updated in each iteration. At the same time, the links between the updated vertices and all other vertices are drawn anew with a fitness-dependent connection probability. We show analytically and numerically that the system self-organizes to a non-trivial state that differs from what is obtained when the two processes are decoupled. A power-law decay of dynamical and topological quantities above a threshold emerges spontaneously, as well as a feedback between different dynamical regimes and the underlying correlation and percolation properties of the network. The properties of dynamical processes defined on complex networks exhibit a strong dependence on the topology1–4. On the other hand, there is growing empirical evidence5–7 that many networks are in turn shaped by some variable associated with each vertex, an aspect captured by the ‘fitness ’ or ‘hidden-variable’ model8,9. Until now, these two facets of the same problem have been treated as separate, by considering on one hand dynamica