Robustness of Preferential-Attachment Graphs: Shifting the Baseline

The widely used characterization of scale-free networks as "robust-yetfragile" originates primarily from experiments on instances generated by preferential attachment. According to this characterization, scale-free networks are more robust against random failures but more fragile against targeted attacks when compared to random networks of the same size. Here, we consider a more appropriate baseline by requiring that the random networks match not only the size but also the inherent minimum degree of preferential-attachment networks they are compared with. Under this more equitable condition, we can (1) prove that random networks are almost surely robust against any vertex removal strategy and (2) show through extensive experiments that scale-free networks generated by preferential attachment are not particularly robust against random failures.