Fig. 3: The scaling of the critical point for scale-free networks.
We simulate random tile damage on randomly embedded scale-free (SF) networks with increasing size N and fixed tile density ρ, and we measure the location of the critical point, \({f}_{{{{\rm{t}}}}}^{* }\), by finding the maximum of the second largest component. We show the scaling of \({f}_{{{{\rm{t}}}}}^{* }\) with N for (a) D = 2 and (b) D = 3 dimensions: markers represent numerical simulations, dashed lines represent the scaling ~ N−(τ−1)/D predicted by Eq. (16) for networks with diverging 〈d2〉, and the dotted lines represent the scaling N−1/D predicted for networks with finite 〈d2〉. We generated networks using c = 4 and ρ = 4, the markers represent the average of 50 independent runs, and the error bars represent their standard deviation.
