Probabilistic prediction in scale-free networks: Diameter changes

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In complex systems, responses to small perturbations are too diverse to predict how much they would be definitely, and then such diverse responses can be predicted in a probabilistic way. Here we study such a problem in scale-free networks, for example, the diameter changes by the deletion of each node for various in silico and real world scale-free networks. We find that the diameter changes are indeed diverse and exhibit an algebraic decay with an exponent ζasymptotically. Interestingly, the exponent ζis robust as ζ≃ 2.2(1) for most scale-free networks, insensitive to the degree exponents γas long as 2 < γ≤ 3. However, there is another type with ζ≃ 1.7(1) and its examples include the Internet and its related in silico model.