A Self–organized model for network evolution Coupling network evolution and extremal dynamics

Here we provide a detailed analysis, along with some extensions and additonal investigations, of a recently proposed [1] self–organised model for the evolution of complex networks. Vertices of the network are characterised by a fitness variable evolving through an extremal dynamics process, as in the Bak–Sneppen [2] model representing a prototype of Self–Organized Criticality. The network topology is in turn shaped by the fitness variable itself, as in the fitness network model [3]. The system self–organizes to a nontrivial state, characterized by a power–law decay of dynamical and topological quantities above a critical threshold. The interplay between topology and dynamics in the system is the key ingredient leading to an unexpected behaviour of these quantities. PACS. 89.75.Hc Networks and genealogical trees – 05.65+b Criticality, self-organized