Self-organized networks as a representation of quantum statistics

A new class of self organized networks is described that is relevant to und erstand the emerging order in a large number of complex systems such as gro wing biological systems, the web, and heterogeneous phases of correlated co ndensed matter systems formed by doping. The Bose and Fermi quantum distrib utions are shown to be the right tool to describe the two extreme limit dis tributions, the fermionic Cayley-tree network and the bosonic scale-free ne twork. 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.