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

TL;DR

This paper investigates the role of long-range links in scale-free networks and finds that short-range links are more critical for maintaining the small-world property, challenging previous assumptions.

Contribution

It reveals that short-range links, rather than long-range links, are primarily responsible for the small-world phenomenon in scale-free networks.

Findings

Scale-free networks are more sensitive to attacks on short-range links.

Long-range links are less critical for the small-world property.

The small-world phenomenon mainly depends on short-range links.

Abstract

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.