Quantum statistics in complex networks.

In this work we discuss the symmetric construction of bosonic and fermionic networks and we present a case of a network showing a mixed quantum statistics. This model takes into account the different nature of nodes, described by a random parameter that we call energy, and includes rewiring of the links. The system described by the mixed statistics is an inhomogeneous system formed by two class of nodes. In fact there is a threshold energy epsilon(s) such that nodes with lower energy (epsilon<epsilon(s)) increase their connectivity, while nodes with higher energy (epsilon>epsilon(s)) decrease their connectivity in time.