Figure 4

Multi-node attacks on N-stable and (N-1)-stable UCTE networks. (a) Nine-random-node removal from the 2r region; (b) nine-random-node removal from the entire network; (c) nine-center-node removal with stochastic capacity allocation; (d) nine-highest-load-node removal with stochastic capacity allocation. Each removal scenario contains 500 repetitions on N-stable (α = 0.5927) and on (N-1)-stable (ε = 0.1) UCTE networks. For clarity purposes the sizes of the surviving giant component recorded at each trial are sorted in non-decreasing order. (e) Comparison of stochastic search for optimal capacity allocation (red circle) with uniform capacity allocation (black line) for nine-center-node attacks on N-stable UCTE network with α = 0.5927 and 500 trials. (f) Comparison of stochastically optimized (red circle) and non-optimized uniform (black circle) capacity allocation against various tightly-clustered nine-node attacks with 1230 repetitions. The lines illustrate the average performance of each allocation.