Co-evolution of networks and quantum dynamics:a generalization of the Barabási-Albert model of preferential attachment

We propose a network growth algorithm based on the dynamics of a quantum mechanical system co-evolving together with a graph which is seen as its phase space. The algorithm naturally generalizes Barab\'asi-Albert model of preferential attachment and it has a rich set of tunable parameters -- for example, the initial conditions of the dynamics or the interaction of the system with its environment. We observe that the algorithm can grow networks with two-modal power-law degree distributions and super-hubs.