  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.
