Self-organized networks as a representation of quantum statistics

A new class of self organized networks is described that is relevant to understand the emerging order in a large number of complex systems such as growing biological systems, the web, and heterogeneous phases of correlated condensed matter systems formed by doping. The Bose and Fermi quantum distributions are shown to be the right tool to describe the two extreme limit distributions, the fermionic Cayley-tree network and the bosonic scale-free network. In this new large class of self-organized networks the two different types of self organization coexists, maintaining the same 'ergodic' nature and are described by a 'mixed' quantum distribution.