  With increasingly ambitious initiatives such as GENI and FIND that seek to
design the future Internet, it becomes imperative to define the characteristics
of robust topologies, and build future networks optimized for robustness. This
paper investigates the characteristics of network topologies that maintain a
high level of throughput in spite of multiple attacks. To this end, we select
network topologies belonging to the main network models and some real world
networks. We consider three types of attacks: removal of random nodes, high
degree nodes, and high betweenness nodes. We use elasticity as our robustness
measure and, through our analysis, illustrate that different topologies can
have different degrees of robustness. In particular, elasticity can fall as low
as 0.8% of the upper bound based on the attack employed. This result
substantiates the need for optimized network topology design. Furthermore, we
implement a tradeoff function that combines elasticity under the three attack
strategies and considers the cost of the network. Our extensive simulations
show that, for a given network density, regular and semi-regular topologies can
have higher degrees of robustness than heterogeneous topologies, and that link
redundancy is a sufficient but not necessary condition for robustness.
