Colloquium on May 5th, 2008Guido Caldarelli University of Rome Selforganized 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 evolution model with the rules of the socalled fitness network model 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 fitnessdependent connection probability. We show analytically and numerically that the system selforganizes to a nontrivial state that differs from what is obtained when the two processes are decoupled. A powerlaw 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. 


