Decapitation of networks with and without weights and direction: The economics of iterated attack and defense

Vulnerability of networks against one-shot decapitation attacks has been addressed several times in the literature. A first study on how a network can best defend itself by replenishing nodes and rewiring edges after decapitation was made by Nagaraja and Anderson. We extend the work of those authors on iterated attack and defense by: (i) considering weighted and directed networks; (ii) taking into account the economic aspects of the attack and defense strategies, namely the cost of node destruction/replenishment and a subtler cost such as the average path length increase. Extensive empirical work is reported which, among other things, shows the importance of obfuscating the network topology.