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Cascading failure in Watts–Strogatz small-world networks


  • Xia, Yongxiang
  • Fan, Jin
  • Hill, David


In this paper, we study the cascading failure in Watts–Strogatz small-world networks. We find that this network model has a heterogeneous betweenness distribution, although its degree distribution is homogeneous. Further study shows that this small-world network is robust to random attack but fragile to intentional attack, in the cascading failure scenario. With comparison to standard random graph and scale-free networks, our result indicates that the robust yet fragile property in the cascading failure scenario is mainly related to heterogeneous betweenness, rather than the network degree distribution. Thus, it suggests that we have to be very careful when we use terms such as homogeneous network and heterogeneous network, unless the distribution we refer to is specified.

Suggested Citation

  • Xia, Yongxiang & Fan, Jin & Hill, David, 2010. "Cascading failure in Watts–Strogatz small-world networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(6), pages 1281-1285.
  • Handle: RePEc:eee:phsmap:v:389:y:2010:i:6:p:1281-1285
    DOI: 10.1016/j.physa.2009.11.037

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    References listed on IDEAS

    1. Xu, Jian & Wang, Xiao Fan, 2005. "Cascading failures in scale-free coupled map lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 349(3), pages 685-692.
    2. R. Kinney & P. Crucitti & R. Albert & V. Latora, 2005. "Modeling cascading failures in the North American power grid," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 46(1), pages 101-107, July.
    3. Crucitti, Paolo & Latora, Vito & Marchiori, Massimo & Rapisarda, Andrea, 2004. "Error and attack tolerance of complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(1), pages 388-394.
    4. Wang, Jianwei & Rong, Lili & Zhang, Liang & Zhang, Zhongzhi, 2008. "Attack vulnerability of scale-free networks due to cascading failures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(26), pages 6671-6678.
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    Cited by:

    1. Caccioli, Fabio & Farmer, J. Doyne & Foti, Nick & Rockmore, Daniel, 2015. "Overlapping portfolios, contagion, and financial stability," Journal of Economic Dynamics and Control, Elsevier, vol. 51(C), pages 50-63.
    2. Foti, Nicholas J. & Pauls, Scott & Rockmore, Daniel N., 2013. "Stability of the World Trade Web over time – An extinction analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 37(9), pages 1889-1910.
    3. Fabio Caccioli & J. Doyne Farmer & Nick Foti & Daniel Rockmore, 2013. "How interbank lending amplifies overlapping portfolio contagion: A case study of the Austrian banking network," Papers 1306.3704,
    4. Zhang, Wenping & Xia, Yongxiang & Ouyang, Bo & Jiang, Lurong, 2015. "Effect of network size on robustness of interconnected networks under targeted attack," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 435(C), pages 80-88.
    5. repec:eee:reensy:v:117:y:2013:i:c:p:1-8 is not listed on IDEAS
    6. Xia, Yongxiang & Zhang, Wenping & Zhang, Xuejun, 2016. "The effect of capacity redundancy disparity on the robustness of interconnected networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 561-568.


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