We study the robustness of complex networks subject to edge removal. Several network models and removing strategies are simulated. Rather than the existence of the giant component, we use total connectedness as the criterion of breakdown. The network
topologies are introduced a simple traffic dynamics and the total connectedness is interpreted not only in the sense of topology but also in the sense of function. We define the topological robustness and the functional robustness, investigate their combined effect and compare their relative importance to each other. The results of our study provide an alternative view of the overall robustness and highlight efficient ways to improve the robustness of the network models.
