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Co-evolution exhibited by a network system, involving the intricate interplaybetween the dynamics of the network itself and the subsystems connected by it,is a key concept for understanding the self-organized, flexible nature ofreal-world network systems. We propose a simple model of such co-evolvingnetwork dynamics, in which the diffusion of a resource over a weighted networkand the resource-driven evolution of the link weights occur simultaneously. Wedemonstrate that, under feasible conditions, the network robustly acquiresscale-free characteristics in the asymptotic state. Interestingly, in the casethat the system includes dissipation, it asymptotically realizes a dynamicalphase characterized by an organized scale-free network, in which the ranking ofeach node with respect to the quantity of the resource possessed therebychanges ceaselessly. Our model offers a unified framework for understandingsome real-world diffusion-driven network systems of diverse types.

Scale-Free Structure Emerging from Co-Evolution of a Network and the Concentration of Diffusive Resources on It