Probabilistic Prediction in Scale-Free Networks: Diameter Changes

In complex systems, responses to small perturbations are too diverse to definitely predict how much they would be, 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 a single vertex for various in silico and real-world scale-free networks. We find that the diameter changes are indeed diverse and their distribution exhibits an algebraic decay with an exponent [Formula presented] asymptotically. Interestingly, the exponent [Formula presented] is robust as [Formula presented] for most scale-free networks and insensitive to the degree exponents [Formula presented] as long as [Formula presented]. However, there is another type with [Formula presented] and its examples include the Internet and its related in silico model.