Model for cascading failures in complex networks

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 69, Issue 4, 2004, Pages 4-

  Crucitti, Paolo ^a   Latora, Vito ^b   Marchiori, Massimo ^c  

^a SCUOLA SUPERIORE DI CATANIA   (Italy)

^b UNIVERSITY OF CATANIA   (Italy)

^c MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84999807972     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.69.045104     Document Type: Article

References (33)

1. S.N. Dorogovtesev and J.F.F. Mendes, Evolution of Networks (Oxford University Press, Oxford, 2003).
2. S.H. Strogatz, Nature (London) 410, 268 (2001).
3. V. Jacobson, Comput. Commun. Rev. 18, 314 (1988).
4. R. Guimerà, A. Arenas, A. Díaz-Guilera, and F. Giralt, Phys. Rev. E 66, 026704 (2002).
5. B.A. Carreras, D.E. Newman, I. Dolrou, and A.B. Poole, in Proceedings of Hawaii International Conference on System Sciences, Maui, Hawaii, 2000.
6. M.L. Sachtjen, B.A. Carreras, and V.E. Lynch, Phys. Rev. E 61, 4877 (2000).
7. J. Glanz and R. Perez-Pena, “90 Seconds That Left Tens of Millions of People in the Dark,” New York Times, August 26, 2003.
8. D.J. Watts, Proc. Natl. Acad. Sci. U.S.A. 99, 5766 (2002).
9. R. Albert, H. Jeong, and A.-L. Barabási, Nature (London) 406, 378 (2000);
10. Nature (London)R. AlbertH. JeongA.-L. Barabási409, 542(E) (2001).
11. P. Holme, B.J. Kim, C.N. Yoon, and S.K. Han, Phys. Rev. E 65, 056109 (2002).
12. P. Crucitti, V. Latora, M. Marchiori, and A. Rapisarda, Physica A 320, 622 (2003).
13. M. Girvan and M.E.J. Newman, Proc. Natl. Acad. Sci. U.S.A. 99, 8271 (2002).
14. A.E. Motter, T. Nishikawa, and Y. Lai, Phys. Rev. E 66, 065103 (2002).
15. A.E. Motter and Y. Lai, Phys. Rev. E 66, 065102(R) (2002).
16. Y. Moreno, R. Pastor-Satorras, A. Vázquez, and A. Vespignani, Europhys. Lett. 62, 292 (2003).
17. Y. Moreno, J.B. Gomez, and A.F. Pacheco, Europhys. Lett. 58, 630 (2002).
18. V. Latora and M. Marchiori, Phys. Rev. Lett. 87, 198701 (2001).
19. S. Wasserman and K. Faust, Social Networks Analysis (Cambridge University Press, Cambridge, 1994).
20. The model can be easily generalized to directed graphs.
21. In the case of an unweighted graph (Formula presented) is 1 if there is an arc joining node i to node j, and 0 otherwise.
22. J. Smith, Commun. ACM 31, 1202 (1988).
23. R. Jain, The Art of Computer Systems Performance Analysis (Wiley, New York, 1991).
24. The harmonic composition of N numbers (Formula presented) is defined as (Formula presented)
25. K.-I. Goh, B. Kahng, and D. Kim, Phys. Rev. Lett. 87, 278701 (2001).
26. Another possibility which gives the same results is to set (Formula presented)
27. As an initial damage to the network here we consider the removal of a node, although the dynamics of the model can be started by the removal of one arc if one wants to simulate, for instance, the breakdown of a line in an electrical power grid.
28. P. Erdös and A. Rényi, Publ. Math. (Debrecen) 6, 290 (1959).
29. A.-L. Barabási and R. Albert, Science 286, 509 (1999).
30. For load-based removals in BA scale-free graphs we have found that (Formula presented) is independent of the size of the system. In fact, we have obtained (Formula presented) 1.3±0.05, 1.28±0.05, respectively, for (Formula presented) 2000, 2500. Such a result is similar to that which is obtained in a simpler model, the fiber-bundle model, studied in Ref. 16.
31. R. Pastor-Satorras, A. Vázquez, and A. Vespignani, Phys. Rev. Lett. 87, 258701 (2001).
32. http://moat.nlanr.net/AS/Data/ASconnlist.20000102.946809601.
33. D.J. Watts and S.H. Strogatz, Nature (London) 393, 440 (1998).