Vertex overload breakdown in evolving networks

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

Volumn 65, Issue 6, 2002, Pages

  Holme, Petter ^a   Kim, Beom Jun ^a,b  

^a UMEÅ UNIVERSITY   (Sweden)

^b Ajou University   (South Korea)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER NETWORKS; DYNAMICS; GEODESY; INTERNET; PROBABILITY; TELECOMMUNICATION NETWORKS;

EVOLVING NETWORKS; POWER-LAW DISTRIBUTION; TRANSPORT FLOW; VERTICES;

GRAPH THEORY;

EID: 37649026650     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.65.066109     Document Type: Article

References (38)

1. For example the graph structure of the neural network of the nematode worm C. Elegans is studied in: L. A. N. Amaral, A. Scala, M. Barthélémy, and H. E. Stanley, Proc. Natl. Acad. Sci. U.S.A. 97, 11149 (2000).
2. R. Albert, H. Jeong, and A.-L. Barabási, Nature (London) 401, 130 (1999).
3. M. Faloutsos, P. Faloutsos, and C. Faloutsos, Comput. Commun. Rev. 29, 251(1999);R. Kumar, P. Rajalopagan, C. Divakumar, A. Tomkins, and E. Upfal, in Proceedings of the 19th Symposium on Principles of Database Systems (Association for Computing Machinery, New York, 1999);
4. A. Broder, Comput. Netw. 33, 309(2000);
5. R. Pastor-Santorras, R. A. Vázquez, and A. Vespignani, Phys. Rev. Lett. 87, 258701 (2001).
6. D. J. Watts and S. H. Strogatz, Nature (London) 393, 440 (1998);D. J. Watts, Small Worlds (Princeton University Press, Princeton, NJ, 1999).
7. D. A. Fell and A. Wagner, Nat. Biotechnol. 18, 1121 (2000);
8. A. Wagner and D. A. Fell, Proc. R. Soc. London, Ser. B 268, 1803 (2001).
9. M. E. J. Newman, Phys. Rev. E 64, 016131 (2001);
10. F. Liljeros, C. R. Edling, L. A. N. Amaral, H. E. Stanley, and Y. Åberg, Nature (London) 411, 907 (2001).
11. M. E. J. Newman, Phys. Rev. E 64, 016132 (2001).
12. R. Cohen, K. Erez, D. ben-Avraham, and S. Havlin, Phys. Rev. Lett. 86, 3682 (2001);
13. Phys. Rev. Lett.D. S. Callaway, M. E. J. Newman, S. H. Strogatz, and D. J. Watts, 85, 5468 (2000).
14. P. Holme, B. J. Kim, C. N. Yoon, and S. K. Han, Phys. Rev. E 65, 056109 (2002).
15. We define avalanche as when the breakdown of one vertex causes an immediate breakdown of other vertices.
16. D. J. Watts, Proc. Natl. Acad. Sci. USA 99, 5766 (2002).
17. Y. Moreno, J. B. Gómez, and A. F. Pacheco, Europhys. Lett. (to be published).
18. See, e.g., S. H. Strogatz, Nature (London) 410, 268 (2001).
19. A.-L. Barabási and R. Albert, Science 286, 509 (1999).
20. A.-L. Barabási, R. Albert, and H. Jeong, Physica A 272, 173 (1999).
21. J. M. Anthonisse, Stichting Mathematisch Centrum Technical Report BN 9/71, 1971 (unpublished);
22. M. L. Freeman, Sociometry40, 35 (1977).
23. Even if betweenness has been used to studdy the load distribution of communication networks [see K.-I. Goh, B. Kahng, and D. Kim, Phys. Rev. Lett. 87, 278201 (2001)], it should be noted that the flow betweenness 18 might be a more relevant measure for information flow, especially in networks (such as the Internet) where load balancing, and not only short path length, governs the network flow. The result of the present model with betweenness replaced by flow betweenness is an interesting open question.
24. L. C. Freeman, S. P. Borgatti, and D. R. White, Social Networks 13, 141 (1991).
25. R. Albert and A.-L. Barabási, Phys. Rev. Lett. 85, 5234 (2000).
26. This is the first principle of some real Internet routing protocols such as the Open Shortest Path First (OSPF) protocol. J. T. Moy, OSPF: Anatomy of an Internet Routing Protocol (Addison-Wesley, Reading, MA, 1998).
27. To calculate the betweenness centrality we use the algorithm presented in U. Brandes, J. Math. Sociol. 25, 163 (2001). An equally efficient algorithm was proposed in Ref. 7.
28. M. E. J. Newman and D. J. Watts, Phys. Lett. A 263, 341 (1999);
29. M. E. J. Newman and D. J. Watts, Phys. Rev. E 60, 7332 (1999);
30. Phys. Rev. EC. Moore and M. E. J. Newman, 61, 5678 (2000);
31. Phys. Rev. EC. MooreM. E. J. Newman62, 7059 (2000);
32. M. Ozana, Europhys. Lett. 55, 762 (2001).
33. M. E. J. Newman, J. Stat. Phys. 101, 819 (2000).
34. In the Erdős-Rényi (ER) model L edges are attached to N vertices with no multiple edges being the only constraint. These networks have an exponential tail of the degree distribution. For the ER model, see P. Erdős and A. Rényi, Publ. Math. Inst. Hung. Acad. Sci. 5, 17 (1960).
35. http://vlado.fmf.uni-lj.si/pub/networks/pajek
36. M. Kihl, Overload Control Strategies for Distributed Communication Networks (Lund University Press, Lund, 1999).
37. C. Huitema, Routing in the Internet, 2nd ed. (Prentice Hall, Upper Saddle River, New Jersey, 2000).
38. H. Jeong, B. Tombor, R. Albert, Z. N. Oltvai, and A.-L. Barabási, Nature (London) 411, 651 (2001).