A high-robustness and low-cost model for cascading failures

We study numerically the cascading failure problem by using artificially created scale-free networks and the real network structure of the power grid. The capacity for a vertex is assigned as a monotonically increasing function of the load (or the betweenness centrality). Through the use of a simple functional form with two free parameters, it is revealed that it is indeed possible to make networks more robust at a lower cost. We suggest that our method to prevent cascade by protecting less vertices is particularly important for the design of more robust real-world networks to cascading failures.