Abstract
Activity-dependent self-organization is the principal mechanism for network formation in some empirical systems. Inspired by previous studies of the brain network formation, we develop a simple model containing concisely the generic mechanism of activity-dependent self-organizing networks. We find that a variety of topologies, including small-world and scale-free graphs, emerges in the equilibrium state of the connecting-disconnecting process. In addition, it is analytically shown how scale-free properties can emerge robustly in such non-growing networks.