Self-Organization and Complex Networks

In this chapter we discuss how the results developed within the theory of fractals and Self–Organized Criticality (SOC) can be fruitfully exploited as ingredients of adaptive network models. In order to maintain the presentation self– contained, we first review the basic ideas behind fractal theory and SOC. We then briefly review some results in the field of complex networks, and some of the models that have been proposed. Finally, we present a self–organized model recently proposed by Garlaschelli et al. [Nat. Phys. 3, 813 (2007)] that couples the fitness network model defined by Caldarelli et al. [Phys. Rev. Lett. 89, 258702 (2002)] with the evolution model proposed by Bak and Sneppen [Phys. Rev. Lett. 71, 4083 (1993)] as a prototype of SOC. Remarkably, we show that the results obtained for the two models separately change dramatically when they are coupled together. This indicates that self–organized networks may represent an entirely novel class of complex systems, whose properties cannot be straightforwardly understood in terms of what we have learnt so far.