  In a recent work [Proc. Natl. Acad. Sci. USA 108, 3838 (2011)], the authors
proposed a simple measure for network robustness under malicious attacks on
nodes. With a greedy algorithm, they found the optimal structure with respect
to this quantity is an onion structure in which high-degree nodes form a core
surrounded by rings of nodes with decreasing degree. However, in real networks
the failure can also occur in links such as dysfunctional power cables and
blocked airlines. Accordingly, complementary to the node-robustness measurement
($R_{n}$), we propose a link-robustness index ($R_{l}$). We show that solely
enhancing $R_{n}$ cannot guarantee the improvement of $R_{l}$. Moreover, the
structure of $R_{l}$-optimized network is found to be entirely different from
that of onion network. In order to design robust networks resistant to more
realistic attack condition, we propose a hybrid greedy algorithm which takes
both the $R_{n}$ and $R_{l}$ into account. We validate the robustness of our
generated networks against malicious attacks mixed with both nodes and links
failure. Finally, some economical constraints for swapping the links in real
networks are considered and significant improvement in both aspects of
robustness are still achieved.
