Range-based attack on links in scale-free networks: are long-range links responsible for the small-world phenomenon?

The small-world phenomenon in complex networks has been identified as being due to the presence of long-range links, i.e., links connecting nodes that would otherwise be separated by a long node-to-node distance. We find, surprisingly, that many scale-free networks are more sensitive to attacks on short-range than on long-range links. This result, besides its importance concerning network efficiency and/or security, has the striking implication that the small-world property of scale-free networks is mainly due to short-range links.