Bose-Einstein condensation in complex networks

The evolution of many complex systems, including the world wide web, business and citation networks is encoded in the dynamic web describing the interactions between the system’s constituents. Despite their irreversible and non-equilibrium nature these networks follow Bose statistics and can undergo Bose-Einstein condensation. Addressing the dynamical properties of these non-equilibrium systems within the framework of equilibrium quantum gases predicts that the ‘first-mover-advantage’, ‘fit-get-rich’ and ‘winner-takes-all’ phenomena observed in competitive systems are thermodynamically distinct phases of the underlying evolving networks.