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

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 66, Issue 6, 2002, Pages 4-

  Motter, Adilson E ^a   Nishikawa, Takashi ^a   Lai, Ying Cheng ^a  

^a ARIZONA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONNECTING NODES; LONG-RANGE LINKS; NUMERICAL COMPUTATIONS; SCALE-FREE NETWORKS;

COMMUNICATION SYSTEMS; COMPUTER NETWORKS; NUMERICAL METHODS;

LARGE SCALE SYSTEMS;

ARTICLE;

EID: 37649030420     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.66.065103     Document Type: Article

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20. We choose to sort the links according to the initial distribution of ranges, instead of an updated distribution, because we want to address the relative importance of short-range and long-range links for the original network. In addition, in terms of attack efficiency, updating is time consuming.
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22. Indeed, the range of a link can be regarded as the length of the second shortest path between the nodes that are connected to the link. Since we are considering the semirandom model, for which everything other than the connectivity distribution is random, the length of the second shortest path should also be correlated with the product of connectivities.
23. For pairs of nodes connected by (Formula presented) shortest paths, the contribution to the load due to each path is (Formula presented)
24. In this model, we start with N nodes and zero links. Then for each pair of nodes, with probability p, we add a link between them. The resulting network has on average (Formula presented) links per node.
25. The same tendency displayed in Figs. 22 and 44 was observed for larger fractions of removed links. In particular, short-range attack is still the most effective one for scale-free networks with scaling exponent around 3. We observe, however, that the removed fraction shown in these figures is already unrealistically large for many practical situations.
26. Reference 15 also considers local strategies of attack.
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