the effect on such a network of a centrality attack. Here the largest connected component retains about 400 nodes until the network suddenly partitions at 14 rounds, whereafter a largest-component size of about 200 is maintained stably.

\[htbp\] ![Average inverse geodesic lengths of rings and clique adaption, under centrality attack []{data-label="fig:BA02a"}](vertex-order-centrality-attack-rings-cliques-geodesic.eps "fig:")\

Some insight into the internal mechanics can be gleaned from Figure \[fig:BA02a\]. This shows the [*average inverse geodesic length*]{}. For each node, we find the length of the shortest path to each other node, and take the inverse (we take the length to be infinite, and thus the inverse to be zero, if the nodes are in disjoint components). We average this value over all $n(n-1)/2$ pairs of nodes. This value falls sharply for defense without adaptation, and falls steadily for defense with rings. These falls reflect increasing difficulty in internode communication. With cliques, the vertex-order attack has little effect, while the centrality attack makes steadily increasing progress on a graph of 400 vertices, until it achieves partition and reduces the largest component to about 200 vertices. But it makes only slow progress thereafter.

Clique sizes
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We next ran a simulation comparing how well defense works when 