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The European Physical Journal D

, Volume 54, Issue 1, pp 87–93 | Cite as

Load-dependent random walks on complex networks

  • L. Wu
  • S. ZhuEmail author
Nonlinear Dynamics

Abstract

Load-dependent random walks are used to investigate the evolution of load distribution in transportation network systems. The walkers hop to a node according to node load of the last time step. The preference of walks leads to a change in the load distribution. It changes from degree-dependent distribution in the case of non-preference walks to eigenvector-centrality-dependent distribution. By numerical simulations, it is shown that the network heterogeneity has a influence on the effect of walk preference. In the cascading failure phenomenon, an appropriate degree correlation can guarantee a low risk of cascading failures.

PACS

05.40.Fb Random walks and Levy flights 89.75.Hc Networks and genealogical trees 05.10.-a Computational methods in statistical physics and nonlinear dynamics 

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References

  1. A.-L. Barabási, R. Albert, Science 286, 509 (1999) Google Scholar
  2. R. Albert, A.-L. Barabási, Rev. Mod. Phys. 74, 47 (2002) Google Scholar
  3. M.E.J. Newman, SIAM Rev. 45, 167 (2003) Google Scholar
  4. S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, D.-U. Hwang, Phys. Rep. 424, 175 (2006) Google Scholar
  5. R. Cohen, K. Erez, D. ben Avraham, S. Havlin, Phys. Rev. Lett. 85, 4626 (2000) Google Scholar
  6. D.S. Callaway, M.E.J. Newman, S.H. Strogatz, D.J. Watts, Phys. Rev. Lett. 85, 5468 (2000) Google Scholar
  7. B. Shargel, H. Sayama, I.R. Epstein, Y. Bar-Yam, Phys. Rev. Lett. 90, 068701 (2003) Google Scholar
  8. P. Holme, B.J. Kim, C.N. Yoon, S.K. Han, Phys. Rev. E 65, 056109 (2002) Google Scholar
  9. K.-I. Goh, D.-S. Lee, B. Kahng, D. Kim, Phys. Rev. Lett. 91, 148701 (2003) Google Scholar
  10. Y. Moreno, J.B. Gómez, A.F. Pacheco, Europhys. Lett. 58, 630 (2002) Google Scholar
  11. E.J. Lee, K.-I. Goh, B. Kahng, D. Kim, Phys. Rev. E 71, 056108 (2005) Google Scholar
  12. A.E. Motter, Y.-C. Lai, Phys. Rev. E 66, 065102 (2002) Google Scholar
  13. L.K. Gallos, R. Cohen, P. Argyrakis, A. Bunde, S. Havlin, Phys. Rev. Lett. 94, 188701 (2005) Google Scholar
  14. A.E. Motter, Phys. Rev. Lett. 93, 098701 (2004) Google Scholar
  15. M. Schafer, J. Scholz, M. Greiner, Phys. Rev. Lett. 96, 108701 (2006) Google Scholar
  16. L. Zhao, K. Park, Y.-C. Lai, Phys. Rev. E 70, 035101 (2004) Google Scholar
  17. K.-I. Goh, B. Kahng, D. Kim, Phys. Rev. Lett. 87, 278701 (2001a) Google Scholar
  18. B.D. Hughes, Random walks and random environments (Clarendon Press, Oxford, New York, 1996), Vol. 1, 2 Google Scholar
  19. E. Almaas, R.V. Kulkarni, D. Stroud, Phys. Rev. E 68, 056105 (2003) Google Scholar
  20. S. Jespersen, I.M. Sokolov, A. Blumen, Phys. Rev. E 62, 4405 (2000) Google Scholar
  21. N. Masuda, N. Konno, Phys. Rev. E 69, 066113 (2004) Google Scholar
  22. R. Burioni, D. Cassi, J. Phys. A: Math. Gen. 38, R45 (2005) Google Scholar
  23. J.D. Noh, H. Rieger, Phys. Rev. Lett. 92, 118701 (2004) Google Scholar
  24. P. Bonacich, J. Math. Sociol. 2, 113 (1972) Google Scholar
  25. P. Bonacich, Am. J. Sociol. 92, 1170 (1987) Google Scholar
  26. M.E.J. Newman, Phys. Rev. E 70, 056131 (2004) Google Scholar
  27. P. Holme, Adv. Compl. Syst. 6, 163 (2003) Google Scholar
  28. E. Estrada, J.A. Rodriguez-Velazquez, Phys. Rev. E 71, 056103 (2005) Google Scholar
  29. K.-I. Goh, B. Kahng, D. Kim, Phys. Rev. E 64, 051903 (2001b) Google Scholar
  30. P. Bonacich, Social Networks 29, 555 (2007) Google Scholar
  31. P. Erdös, A. Rényi, Publ. Math. Inst. Hung. Acad. Sci 5, 17 (1960) Google Scholar
  32. D.J. Watts, S.H. Strogatz, Nature 393, 440 (1998) Google Scholar
  33. A.-L. Barabási, R. Albert, H. Jeong, Physica A 272, 173 (1999) Google Scholar
  34. M.E.J. Newman, Phys. Rev. Lett. 89, 208701 (2002) Google Scholar
  35. R. Xulvi-Brunet, I.M. Sokolov, Phys. Rev. E 70, 066102 (2004) Google Scholar
  36. M.E.J. Newman, Social Networks 27, 39 (2005) Google Scholar
  37. Z. Zhang, Y. Qi, S. Zhou, W. Xie, J. Guan, Phys. Rev. E 79, 021127 (2009) Google Scholar
  38. F.A. Torres, M.G. Gauthier, G.W. Slater, Phys. Rev. E 78, 065701 (2008) Google Scholar
  39. C. Tojo, P. Argyrakis, Phys. Rev. E 54, 58 (1996) Google Scholar
  40. C.P. Herrero, Phys. Rev. E 71, 016103 (2005) Google Scholar
  41. S.-J. Yang, Phys. Rev. E volume71, 016107 (2005) Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.School of Physical Science and Technology, Suzhou UniversityJiangsuP.R. China

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