Quantum-Classical Transition in Complex Networks

The inherent properties of specific physical systems can be used as metaphors for investigation of the behavior of complex networks. This insight has already been put into practice in previous work, e.g., studying the network evolution in terms of phase transitions of quantum gases or representing distances among nodes as if they were particle energies. This paper shows that the emergence of different structures in complex networks, such as the scale-free and the winner-takes-all networks, can be represented in terms of a quantumclassical transition for quantum gases. In particular, we propose a model of fermionic networks that allows us to investigate the network evolution and its dependence on the system temperature. Simulations, performed in accordance with the cited model, clearly highlight the separation between classical random and winnertakes-all networks, in full correspondence with the separation between classical and quantum regions for quantum gases. We deem this model useful for the analysis of synthetic and real complex networks. PACS numbers: 89.75.-k, 89.75.Hc, 05.65.+b ar X iv :1 20 5. 17 71 v3 [ co nd -m at .d is -n n] 1 4 A ug 2 01 4 Quantum-Classical Transitions in Complex Networks 2