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We tested also by taking a few different realizations and keeping the network structures and changing only the attack order. The results have been found to be very similar, as seen in Fig. 8.
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In order to estimate the length of the plateau stage, we introduce a method to define the beginning (Equation presented) and the end (Equation presented) of the plateau in each realization. In Fig. 3(a) we find the time step (Equation presented) of the first local minimum and (Equation presented) of the last local minimum. Then we define a threshold (Equation presented), which is twice the average failure size between these two minimums. This is because the (Equation presented) values always have some random fluctuations above or below the mean value, which should be the same order as the mean. Therefore, we use twice the mean as the threshold for including such fluctuations. Then we define (Equation presented) and (Equation presented) as the first time step and the last one where (Equation presented).
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In order to estimate the length of the plateau stage, we introduce a method to define the beginning (Equation presented) and the end (Equation presented) of the plateau in each realization. In Fig. 3(a) we find the time step (Equation presented) of the first local minimum and (Equation presented) of the last local minimum. Then we define a threshold (Equation presented), which is twice the average failure size between these two minimums. This is because the (Equation presented) values always have some random fluctuations above or below the mean value, which should be the same order as the mean. Therefore, we use twice the mean as the threshold for including such fluctuations. Then we define (Equation presented) and (Equation presented) as the first time step and the last one where (Equation presented).
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