  The increasing demands in security and reliability of infrastructures call
for the optimal design of their embedded complex networks topologies. The
following question then arises: what is the optimal layout to fulfill best all
the demands? Here we present a general solution for this problem with
scale-free networks, like the Internet and airline networks. Precisely, we
disclose a way to systematically construct networks which are 100$\%$ robust
against random failures as well as to malicious attacks. Furthermore, as the
sizes of these networks increase, their shortest paths become asymptotically
invariant and densities of links go to zero, making them ultra-small worlds and
highly sparse, respectively. The first property is ideal for communication and
navigation purposes, while the second is interesting economically.

Physics and Society;Social and Information Networks