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Phys. Rev. Lett. 94, 188701 (2005)

Stability and Topology of Scale-Free Networks under Attack and Defense Strategies

Lazaros K. Gallos,1 Reuven Cohen,2 Panos Argyrakis,1 Armin Bunde,3 and Shlomo Havlin2

1Department of Physics, University of Thessaloniki, 54124 Thessaloniki, Greece
2Minerva Center and Department of Physics, Bar-Ilan University, 52900 Ramat-Gan, Israel
3Institut f?r Theoretische Physik III, Justus-Liebig-Universit?t Giessen, Heinrich-Buff-Ring 16, 35392 Giessen, Germany

(Received 16 September 2004; published 10 May 2005)

We study tolerance and topology of random scale-free networks under attack and defense strategies that depend on the degree k of the nodes. This situation occurs, for example, when the robustness of a node depends on its degree or in an intentional attack with insufficient knowledge of the network. We determine, for all strategies, the critical fraction pc of nodes that must be removed for disintegrating the network. We find that, for an intentional attack, little knowledge of the well-connected sites is sufficient to strongly reduce pc. At criticality, the topology of the network depends on the removal strategy, implying that different strategies may lead to different kinds of percolation transitions. ?2005 The American Physical Society

URL: http://link.aps.org/abstract/PRL/v94/e188701
PACS: 89.75.Hc, 87.23.Ge, 89.20.Hh

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