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Complex Network Reliability Analysis based on Entropy Theory

Volume 15, Number 6, June 2019, pp. 1642-1651
DOI: 10.23940/ijpe.19.06.p15.16421651

Kai Lia, Wei Wub, and Fusheng Liua

aDepartment of Technical Support Engineering, Army Armored Force Academy, Beijing, 100072, China
bInstitute of Beijing Special Vehicle, Beijing, 100072, China

 

(Submitted on December 15, 2018; Revised on January 16, 2019; Accepted on February 18, 2019)

Abstract:

Network reliability is an essential issue of complex networks; the reliability of complex networks plays an important role in the performance in the research process. At the same time, the number of connected nodes in a complex network is a main measure of the complex network. Due to the randomness of complex networks, we define one new degree sequence and the entropy of the complex network, and we then study the entropy of the network as a new measure for the network reliability. The features of entropy are studied in complex networks, and entropy is analyzed in two representative complex network models, the random network model and scale-free network model. The degree distributions functions in the random network model and scale-free network model have significantly different characteristics, the Poisson distribution and Power-law distribution. Furthermore, we study the entropy features under two nodes fault models, random failures and deliberate attacks. We discuss the entropy of the random network model and scale-free network model in two fault modes with the fault intensity gradually increasing from 0 to 1.0. Then, we study the relation between the average degree distribution and the entropy of the network when the fault intensity is 0.3. The results show that the entropy of the network is reasonable to measure the network reliability similar to the number of connected nodes in the network. The purpose of the research is to provide a new way to study network reliability.

 

References: 33

  1. S. R. Pastor and A. Vespignani, “Evolution and Structure of the Internet: A Statistical Physics Approach,” Cambridge University Press, Cambridge, 2004
  2. R. Kinney, P. Crucitti, R. Albert, and V. Latora, “Modeling Cascading Failures in the North American Power Grid,” The European Physical Journal B, Vol. 46, No. 5, pp. 101-107, May 2005
  3. S. H. Strogatz, “Exploring Complex Networks,” Nature, Vol. 410, No. 6825, pp. 268-276, August 2001
  4. L. S. Wu, Q. M. Tan, and Y. H. Zhang, “Network Connectivity Entropy and its Application on Network Connectivity Reliability,” Physica A, Vol. 392, No. 7, pp. 5536-5541, July 2013
  5. R. Albert, H. Jeong, and A. L. Barabási, “Attack and Error Tolerance of Complex Networks,” Nature, Vol. 406, pp. 378-382, May 2000
  6. Y. N. Jiang, R. Y. Li, and N. Huang, “Survey on Network Reliability Evaluation Methods,” Computer Science, Vol. 39, No. 2, pp. 9-13, February 2017
  7. R. X. Zhou, S. C. Liu, and W. H Qiu, “Survey of Applications of Entropy in Decision Analysis,” Control and Decision, Vol. 23, No. 4, pp. 361-366, April 2016
  8. R. Albert and A. L. Barabási, “Statistical Mechanics of Complex Network,” Reviews of Modern Physics, Vol. 74, No. 1, pp. 47-97, January 2002
  9. P. Crucitti, V. Latora, M. Marchiori, and A. Rapisarda, “Error and Attack Tolerance of Complex Networks,” Physica A, Vol. 340, No. 4, pp. 388-394, April 2004
  10. P. Erdös and A. Rényi, “On the Evolution of Random Graphs,” Publication of the Mathematical Institute of the Hungarian Academy of Sciences, Vol. 5, pp. 17-61, May 1960
  11. D. J. Watts and S. H. Strogatz, “Collective Dynamics of Human ReliabilitySmall-WorldHuman Reliability Networks,” Nature, Vol. 393, pp. 440-442, June 1998
  12. A. L. Barabási and R. Albert, “Emergence of Scaling in Random Networks,” Science, Vol. 286, pp. 509-512, May 1999
  13. R. Cohen, K. Erez, D. B Avraham, and S. Havlin, “Breakdown of the Internet under Intentional Attack,” Physical Review Letters, Vol. 86, No. 21, pp. 3682-3685, November 2001
  14. G. Szabo, M. Alava, and J. Kertesz, “Structural Transitions in Scale-Free Networks,” Physical Review E, Vol. 67, No. 5, pp. 56-78, May 2003
  15. E. Ravasz and A. L. Barabási, “Hierarchical Organization in Complex Networks,” Physical Review E, Vol. 67, No. 2, pp. 261-278, February 2003
  16. A. Fronczak, J. A. Holyst, and M. Jedynak, “Higher Order Clustering Coefficients in Barabási-Albert Networks,” Physica A, Vol. 316, No. 1, pp. 688-694, January 2002
  17. G. Alfredo and T. Andrea, “On the Reliability Analysis of Systems and Sos: The RAMSAS Method and Related Extensions,” IEEE Systems Journal, Vol. 9, No. 1, pp. 232-241, January 2015
  18. M. Newman, “The Structure and Function of Complex Network,” SIAM Review, Vol. 45, No. 2, pp. 167-189, February 2013
  19. M. Newman, S. H. Strogatz, and D. J. Watts, “Random Graphs with Arbitrary Degree Distributions and their Applications,” Physical Review E, Vol. 64, No. 2, pp. 623-631, February 2001
  20. M. Molloy and B. Reed, “A Critical Point for Random Graphs with a Given Degree Sequence,” Random Structures and Algorithms, Vol. 6, No. 2, pp. 161-179, February 1995
  21. M. Newman and D. J. Watts, “Renormailzation Group Analysis of the Small-World Network Model,” Physics Letters A, Vol. 263, No. 4, pp. 341-346, April 1999
  22. J. M. Kleinberg, “Navigation in s Small World-It is Easier to Find Short Chains Between Points in Some Networks than Others,” Nature, Vol. 406, No. 8, pp. 845-853, August 2000
  23. P. L. Krapivsky, S. Redner, and F. Leyvraz, “Connectivity of Growing Random Networks,” Physical Review Letters, Vol. 85, No. 21, pp. 4629-4632, November 2000
  24. F. T. Boesch and R. E. Thomas, “On Graphs of Invulnerable Communication Nets,” IEEE Transactions on Circuit Theory, Vol. 17, No. 2, pp. 183-192, February 1970
  25. R. S. Wilkov, “Analysis and Design of Reliable Computer Networks,” IEEE Transactions on Circuit Theory, Vol. 20, No. 3, pp. 660-678, 1972
  26. V. Latora and M. Marchiori, “Vulnerability and Protection of Critical Infrastructure,” Physical Review E, Vol. 71, No. 2, pp. 31-42, March 2005
  27. I. Mishkovshi, M. Biey, and L. Kocarev, “Vulnerability of Complex Networks,” Communications in Nonlinear Science and Numerical Simulation, Vol. 16, No. 1, pp. 341-349, January 2011
  28. P. Hu, W. L. Fan, and S. W. Mei, “Identifying Node Importance in Complex Networks,” Physica A, Vol. 429, No. 3, pp. 169-176, March 2015
  29. L. M. Zhang, D. Q. Li, and B. Fu, “Reliability Analysis of Interdependent Lattices,” Physica A, Vol. 452, No. 15, pp. 120-125, August 2016
  30. E. R. Colman and G. J. Rodgers, “Complex Scale-Free Networks with Tunable Power-Law Exponent and Clustering,” Physica A, Vol. 392, No. 2, pp. 5501-5510, February 2013
  31. B. S. Kerner, “Criticism of Generally Accepted Fundamentals and Methodologies of Traffic and Transportation Theory: A Brief Review,” Physica A, Vol. 392, No. 2, pp. 5261-5282, February 2013
  32. O. Y. Min, Z. Z. Pan, and L. Hong, “Correlation Analysis of Different Vulnerability Metrics on Power Grids,” Physica A, Vol. 396, No. 2, pp. 204-211, February 2014
  33. C. G. Ghedini and H. C. Carlos, “Rethinking Failure and Attack Tolerance Assessment in Complex Networks,” Physica A, Vol. 390, No. 23, pp. 4684-4691, December 2017

 

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