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Scientific Programming
Volume 2016 (2016), Article ID 5659687, 7 pages
http://dx.doi.org/10.1155/2016/5659687
Research Article

Optimal Design on Robustness of Scale-Free Networks Based on Degree Distribution

1School of Electrical Engineering and Automation, Jiangsu Normal University, Xuzhou 221116, China
2School of Government, Beijing Normal University, Beijing 100875, China
3People’s Government of Wuduan Town, Peixian, Xuzhou 221638, China

Received 3 April 2016; Revised 7 June 2016; Accepted 5 July 2016

Academic Editor: Meng Guo

Copyright © 2016 Jianhua Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. S. H. Strogatz, “Exploring complex networks,” Nature, vol. 410, no. 6825, pp. 268–276, 2001. View at Publisher · View at Google Scholar · View at Scopus
  2. D. J. Watts and S. H. Strogatz, “Collective dynamics of ‘small-world’ networks,” Nature, vol. 393, no. 6684, pp. 440–442, 1998. View at Publisher · View at Google Scholar · View at Scopus
  3. A.-L. Barabasi and R. Albert, “Emergence of scaling in random networks,” Science, vol. 286, no. 5439, pp. 509–512, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. R. Albert and A.-L. Barabasi, “Statistical mechanics of complex networks,” Reviews of Modern Physics, vol. 74, no. 1, pp. 47–97, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. R. Albert, H. Jeong, and A. L. Barabasi, “Attack and error tolerance of complex networks,” Nature, vol. 406, pp. 378–382, 2000. View at Publisher · View at Google Scholar
  6. S. N. Dorogovtsev and J. F. F. Mendes, “Evolution of networks,” Advance in Physics, vol. 51, no. 4, pp. 1079–1187, 2002. View at Publisher · View at Google Scholar
  7. M. E. Newman, “The structure and function of complex networks,” SIAM Review, vol. 45, no. 2, pp. 167–256, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. L. Zhao, K. Park, and Y.-C. Lai, “Attack vulnerability of scale-free networks due to cascading breakdown,” Physical Review E, vol. 70, no. 3, Article ID 035101, 2004. View at Publisher · View at Google Scholar · View at Scopus
  9. J. W. Wang, L. L. Rong, L. Zhang, and Z. Z. Zhang, “Attack vulnerability of scale-free networks due to cascading failures,” Physica A, vol. 387, no. 26, pp. 6671–6678, 2008. View at Publisher · View at Google Scholar · View at Scopus
  10. S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D.-U. Hwang, “Complex networks: structure and dynamics,” Physics Reports, vol. 424, no. 4-5, pp. 175–308, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. A. E. Motter and Y.-C. Lai, “Cascade-based attacks on complex networks,” Physical Review E, vol. 66, no. 6, Article ID 065102, 2002. View at Publisher · View at Google Scholar · View at Scopus
  12. Z.-H. Wu and H.-J. Fang, “Cascading failures of complex networks based on two-step degree,” Chinese Physics Letters, vol. 25, no. 10, pp. 3822–3825, 2008. View at Publisher · View at Google Scholar · View at Scopus
  13. B. Wang, H. W. Tang, C. H. Guo, and Z. L. Xiu, “Entropy optimization of scale-free networks' robustness to random failures,” Physica A, vol. 363, no. 2, pp. 591–596, 2006. View at Publisher · View at Google Scholar · View at Scopus
  14. J. Wu, Y.-J. Tan, H.-Z. Deng, and D.-Z. Zhu, “Normalized entropy of rank distribution: a novel measure of heterogeneity of complex networks,” Chinese Physics, vol. 16, no. 6, pp. 1576–1580, 2007. View at Publisher · View at Google Scholar · View at Scopus
  15. M. E. J. Newman, S. H. Strogatz, and D. J. Watts, “Random graphs with arbitrary degree distributions and their applications,” Physical Review E, vol. 64, no. 2, Article ID 026118, 2001. View at Google Scholar · View at Scopus
  16. R. Cohen, K. Erez, D. Ben-Avraham, and S. Havlin, “Resilience of the Internet to random breakdowns,” Physical Review Letters, vol. 85, no. 21, pp. 4626–4628, 2000. View at Publisher · View at Google Scholar · View at Scopus
  17. E. Tsukamoto and S. Shirayama, “Influence of the variance of degree distributions on the evolution of cooperation in complex networks,” Physica A, vol. 389, no. 3, pp. 577–586, 2010. View at Publisher · View at Google Scholar · View at Scopus
  18. T. A. Snijders, “The degree variance: an index of graph heterogeneity,” Social Networks, vol. 3, no. 3, pp. 163–174, 1981. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. J. Wang, “Mitigation of cascading failures on complex networks,” Nonlinear Dynamics, vol. 70, no. 3, pp. 1959–1967, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. J. Wang, “Mitigation strategies on scale-free networks against cascading failures,” Physica A: Statistical Mechanics and its Applications, vol. 392, no. 9, pp. 2257–2264, 2013. View at Publisher · View at Google Scholar · View at Scopus