  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.
