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The increasing demands in security and reliability of infrastructures callfor the optimal design of their embedded complex networks topologies. Thefollowing question then arises: what is the optimal layout to fulfill best allthe demands? Here we present a general solution for this problem withscale-free networks, like the Internet and airline networks. Precisely, wedisclose a way to systematically construct networks which are 100$\%$ robustagainst random failures as well as to malicious attacks. Furthermore, as thesizes of these networks increase, their shortest paths become asymptoticallyinvariant and densities of links go to zero, making them ultra-small worlds andhighly sparse, respectively. The first property is ideal for communication andnavigation purposes, while the second is interesting economically.

Mandala Networks: ultra-robust, ultra-small-world and highly sparse graphs