  Co-evolution exhibited by a network system, involving the intricate interplay
between the dynamics of the network itself and the subsystems connected by it,
is a key concept for understanding the self-organized, flexible nature of
real-world network systems. We propose a simple model of such co-evolving
network dynamics, in which the diffusion of a resource over a weighted network
and the resource-driven evolution of the link weights occur simultaneously. We
demonstrate that, under feasible conditions, the network robustly acquires
scale-free characteristics in the asymptotic state. Interestingly, in the case
that the system includes dissipation, it asymptotically realizes a dynamical
phase characterized by an organized scale-free network, in which the ranking of
each node with respect to the quantity of the resource possessed thereby
changes ceaselessly. Our model offers a unified framework for understanding
some real-world diffusion-driven network systems of diverse types.
