Considering distributed transmission mode of flow and load-capacity relation for edges in real networks,an edge cascading failures model with a tunable weight parameter is proposed. According to new measures to the robustness of a network, cascading failures triggered by intentional edge attacks on two typical complex networks are investigated. The simulation results show the existence of optimal parameter value corresponding to the stron-gest robustness achievement for the networks against edge cascading failures,reducing sig-nificantly the likelihood of the occurrence of catastrophic dynamic...