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Optimal Network Robustness Against Attacks in Varying Degree Distributions

In varying degree distributions, we investigate the optimally robust networks against targeted attacks to nodes with higher degrees. In considering that a network tends to have more robustness with a smaller variance of degree distributions, we clarify the optimal robustness at random regular graphs in their comprehensive discrete or random perturbations. By comparing robustness measurements on them, we find that random regular graphs have the optimal robustness against attacks in varying degree distributions.