Supersymmetric multiplex networks described by coupled Bose and Fermi statistics.

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 any multiplex network. 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 nonequilibrium growing dynamics of the supersymmetric multiplex network with its quantum information static characteristics.