PMID: 11328053May 1, 2001Paper

Breakdown of the internet under intentional attack

Physical Review Letters
R CohenS Havlin

Abstract

We study the tolerance of random networks to intentional attack, whereby a fraction p of the most connected sites is removed. We focus on scale-free networks, having connectivity distribution P(k) approximately k(-alpha), and use percolation theory to study analytically and numerically the critical fraction p(c) needed for the disintegration of the network, as well as the size of the largest connected cluster. We find that even networks with alpha < or = 3, known to be resilient to random removal of sites, are sensitive to intentional attack. We also argue that, near criticality, the average distance between sites in the spanning (largest) cluster scales with its mass, M, as square root of [M], rather than as log (k)M, as expected for random networks away from criticality.

References

Aug 10, 2000·Nature·R AlbertA L Barabasi
Nov 18, 2000·Physical Review Letters·R CohenS Havlin
Jan 3, 2001·Physical Review Letters·D S CallawayD J Watts

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Citations

May 14, 2004·Nature·Stephen EubankNan Wang
Jul 21, 2011·Nature Communications·Gourab Ghoshal, Albert-László Barabási
Jan 24, 2008·Proceedings of the National Academy of Sciences of the United States of America·Jesús Gómez-GardeñesElio Profumo
Mar 4, 2011·Proceedings of the National Academy of Sciences of the United States of America·Christian M SchneiderHans J Herrmann
Jun 26, 2012·Journal of the Royal Society, Interface·Paolo BajardiVittoria Colizza
Sep 6, 2013·Journal of the Royal Society, Interface·Rick QuaxPeter M A Sloot
Sep 26, 2001·Proceedings. Biological Sciences·R V Solé, J M Montoya
Jun 24, 2011·PloS One·Ricardo GutiérrezStefano Boccaletti
Jun 4, 2011·PloS One·Baharan Mirzasoleiman, Mahdi Jalili
Aug 21, 2013·PloS One·Olivia Woolley-MezaDirk Brockmann
Jan 3, 2013·Chaos·Jun WuHong-Zhong Deng
Apr 2, 2009·Chaos·Regino CriadoMaría Vela-Pérez
Jul 7, 2007·Chaos·Liang HuangZhifeng Hu
Oct 2, 2012·The Journal of Chemical Physics·Yuan LinZhongzhi Zhang
Sep 20, 2002·Proceedings of the National Academy of Sciences of the United States of America·Kwang-Il GohDoochul Kim
Jun 26, 2007·Proceedings of the National Academy of Sciences of the United States of America·Shai CarmiEran Shir
Jan 28, 2004·Proceedings of the National Academy of Sciences of the United States of America·Matteo MarsiliFrantisek Slanina
Oct 9, 2002·Proceedings of the National Academy of Sciences of the United States of America·Soon-Hyung YookAlbert-Laszlo Barabasi
Jan 19, 2016·Scientific Reports·Fragkiskos D MalliarosMichalis Vazirgiannis
May 2, 2012·IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics : a Publication of the IEEE Systems, Man, and Cybernetics Society·Benyun Shi, Jiming Liu
Oct 11, 2015·BMC Bioinformatics·Da RuanGiovanni Montana
Jul 2, 2015·Nature·Flaviano Morone, Hernán A Makse
Dec 3, 2014·Journal of Theoretical Biology·Christoforos Hadjichrysanthou, Kieran J Sharkey
Mar 13, 2015·PLoS Computational Biology·Eugenio ValdanoVittoria Colizza
Sep 1, 2015·PloS One·Byungjoon MinHernán A Makse
Sep 25, 2014·PloS One·Christopher PriesterTiago P Peixoto
Nov 17, 2015·PloS One·Bruno Requião da CunhaSebastián Gonçalves
Jul 16, 2016·PLoS Computational Biology·Jose L HerreraLauren Ancel Meyers
Nov 3, 2016·Proceedings of the National Academy of Sciences of the United States of America·Alfredo BraunsteinLenka Zdeborová
Nov 26, 2016·Scientific Reports·Teruyoshi Kobayashi, Naoki Masuda
Sep 10, 2016·Scientific Reports·Shiwen SunChengyi Xia
Nov 30, 2016·Scientific Reports·Lenka ZdeborováHai-Jun Zhou
Oct 8, 2016·Scientific Reports·Mario MuredduHildegard Meyer-Ortmanns
Jul 28, 2016·Scientific Reports·Yilun Shang

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