has been no published work since on how a network can defend itself against a decapitation attack. Here is one possible explanation: the two obvious defences don’t work.

One of these is simply to replenish destroyed nodes with new nodes, and furnish them with edges according to the same scale-free rule that was used to generate the network initially. One might hope that some equilibrium would be found between attack and defence.

The other obvious defence is to replenish destroyed nodes, but to wire their edges according to a random graph model. In this way, we might hope that, under attack, a network would evolve from an efficient scale-free structure into a less efficient but more resilient random structure. In a real application, this might happen either as a result of nodes learning new behaviour, or by selective pressure on a node population with heterogeneous connectivity preferences: in peacetime the nodes with higher degree would become hubs, while in wartime they would be early casualties.

Nice as these ideas may seem in theory, they do not work at all well in practice. Figure \[fig:BA00\] shows first (solid line) how the vertex-order attack of Albert, Jeong and Barabási works against a 