Robustness of preferential-attachment graphs

Abstract The widely used characterization of scale-free networks as “robust-yet-fragile” originates primarily from experiments on instances generated by preferential attachment. According to this characterization, are more robust against random failures but fragile targeted attacks when compared the same size. Here, we consider a appropriate baseline requiring that match not only size also inherent minimum degree preferential-attachment they with. Under equitable condition, can (1) prove almost surely any vertex removal strategy and (2) show through extensive attachment particularly failures. Finally, (3) add demonstrating preferentially attaching well-connected vertices does enhance robustness at all.