Quantum statistics in complex networks
Ginestra Bianconi
Abstract
We show that quantum statistics can be used to describe growing complex networks. The bosonic network is a scale-free network with different qualities of the nodes and a thermal noise while the fermionic network is a growing Cayley tree. The symmetric construction of bosonic and fermionic networks is presented. Morever we present a case of a network showing a mixed quantum statistics. This model takes into a 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 inhomogemeous 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.
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