K-core-preferred attack to the internet: is it more malicious than degree attack?

K-core (k-shell) index is an interesting measure that describes the core and fringe nodes in a complex network. Recent studies have revealed that some high k-core value nodes may play a vital role in information diffusion. As a result, one may expect that attacking high k-core nodes preferentially can collapse the Internet easily. To our surprise, however, the experiments on two Internet AS-level topologies show that: Although a k-core-preferred attack is feasible in reality, it turns out to be less effective than a classic degree-preferred attack. Indeed, as indicated by the measure: normalized susceptibility, we need to remove 2% to 3% more nodes in a k-core-preferred attack to make the network collapsed. Further investigation on the nodes in a same shell discloses that these nodes often have degrees varied drastically, among which there are nodes with high k-core values but low degrees. These nodes cannot contribute many link deletions in an early stage of a k-core-preferred attack, and therefore make it less malicious than a degree-preferred attack.