The effect of two different edge attacks on the robustness of random scale-free networks against cascading failure is investigated by establishing a cascading failure model for random scale-free networks. In this model, the initial load of an edge is defined as a nonlinear function of the product of the betweenness of its end nodes with an adjustable parameter, and the local preferential redistribution rule is applied to assign the broken edge’s load. An interesting conclusion is reached through theoretical analyses and numerical simulations: there is a threshold of the load parameter. W...