Supersymmetric multiplex networks described by coupled Bose and Fermi statistics

Abstract

Until now, no simple symmetries have been detected in complex networks. Here we show that, in growing multiplex networks the symmetries of multilayer structures can be exploited by their dynamical rules, forming supersymmetric multiplex networks described by coupled Bose-Einstein and Fermi-Dirac quantum statistics. The supersymmetric multiplex is formed by layers which are scale-free networks and can display a Bose-Einstein condensation of the links. To characterize the complexity of the supersymmetric multiplex using quantum information tools, we extend the definition of the network entanglement entropy to the layers of multiplex networks. Interestingly we observe a very simple relation between the entanglement entropies of the layers of the supersymmetric multiplex network and the entropy rate of the same multiplex network. This relation therefore connects the classical non equilibrium growing dynamics of the supersymmetric multiplex network with its quantum information static characteristics.

(9 pages, 3 figures)

References in corpus (7)

• The structure and dynamics of multilayer networks
• Hyperbolic Geometry of Complex Networks
• Navigability of Complex Networks
• Avoiding catastrophic failure in correlated networks of networks
• Generalized Bose-Fermi statistics and structural correlations in weighted networks
• Network Cosmology
• Phase transition of light on complex quantum networks