Skip to main content

Comparing the reliability of networks by spectral analysis

Abstract

We provide a method for the ranking of the reliability of two networks with the same connectance. Our method is based on the Cheeger constant linking the topological property of a network with its spectrum. We first analyze a set of twisted rings with the same connectance and degree distribution, and obtain the ranking of their reliability using their eigenvalue gaps. The results are generalized to general networks using the method of rewiring. The success of our ranking method is verified numerically for the IEEE57, the Erdős-Rényi, and the Small-World networks.

This is a preview of subscription content, access via your institution.

References

  1. D. Stauffer, A. Aharony, Introduction to Percolation Theory (Taylor & Francis, London, 1994)

  2. M.E.J. Newman, SIAM Rev. 45, 167 (2003)

    MathSciNet  Article  MATH  ADS  Google Scholar 

  3. R. Cohen, S. Halvin, Complex Networks: Structure, Robustness and Function (Cambridge University Press, Cambridge, 2010)

  4. M.E.J. Newman, Networks: An Introduction (Oxford University Press, Oxford, 2010)

  5. R. Albert, A. Barabási, Rev. Mod. Phys. 74, 47 (2002)

    Article  MATH  ADS  Google Scholar 

  6. S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, D.U. Hwang, Phys. Rep. 424, 175 (2006)

    MathSciNet  Article  ADS  Google Scholar 

  7. S.N. Dorogovtesev, J.F.F. Mendes, Evolution of Networks (Oxford University Press, Oxford, 2003)

  8. R. Pastor-Satorras, A. Vespignani, Evolution and Structure of the Internet: A Statistical Physics Approach (Cambridge University Press, New York, 2004)

  9. G. Caldarelli, Scale-Free Networks (Oxford University Press, Oxford, 2007)

  10. S. Pierre, M.A. Hyppolite, J.M. Bourjolly, O. Dioume, Eng. Appl. Artif. Intel. 8, 61 (1995)

    Article  Google Scholar 

  11. G.A. Walters, D.K. Smith, Eng. Optim. 24, 261 (1995)

    Article  Google Scholar 

  12. N. Masuda, New J. Phys. 11, 123018 (2009)

    Article  ADS  Google Scholar 

  13. J.G. Restrepo, E. Ott, B.R. Hunt, Phys. Rev. Lett. 100, 058701 (2008)

    Article  ADS  Google Scholar 

  14. J. Cheeger, Problems in Analysis (Papers dedicated to Salomon Bochner, 1969) (Princeton University Press, Princeton, 1970)

  15. L. Donetti, F. Neri, M.A. Muñoz, J. Stat. Mech. 08, P08007 (2006)

    Google Scholar 

  16. J. Dodziuk, Trans. Amer. Math. Soc. 284, 787 (1984)

    MathSciNet  Article  MATH  Google Scholar 

  17. N. Alon, V.D. Milman, J. Combin. Theory Ser. B 38, 73 (1985)

    MathSciNet  Article  MATH  Google Scholar 

  18. N. Alon, Combinatorica 6, 83 (1986)

    MathSciNet  Article  MATH  Google Scholar 

  19. Z. Wang, A. Scaglione, R.J. Thomas, IEEE Trans. Smart Grid 1, 28 (2010)

    Article  Google Scholar 

  20. P. Erdős, A. Rényi, Publ. Math. Debrecen 6, 290 (1959)

    MathSciNet  Google Scholar 

  21. P. Erdős, A. Rényi, Magyar Tud. Akad. Mat. Kutató Int. Közl 8, 229 (1963)

    Google Scholar 

  22. The Small World, edited by M. Kochen (Ablex Press, Norwood, 1989)

  23. D.J. Watts, Small Worlds: The Dynamics of Networks between Order and Randomness (Princeton University Press, Princeton, 1999)

  24. T. Watanabe, N. Masuda, Phys. Rev. E 82, 046102 (2010)

    MathSciNet  Article  ADS  Google Scholar 

  25. S. Hoory, N. Linial, A. Wigderson, Bull. Amer. Math. Soc. 43, 439 (2006)

    MathSciNet  Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Kwok Yip Szeto.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Wang, Z., Szeto, K. Comparing the reliability of networks by spectral analysis. Eur. Phys. J. B 87, 234 (2014). https://doi.org/10.1140/epjb/e2014-50498-0

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/e2014-50498-0

Keywords

  • Statistical and Nonlinear Physics