| Original Articles |
|
|
|
|
Cascading Failures of Complex Networks Based on Two-Step Degree |
| WU Zhi-Hai, FANG Hua-Jing |
| Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074 |
|
| Cite this article: |
|
WU Zhi-Hai, FANG Hua-Jing 2008 Chin. Phys. Lett. 25 3822-3825 |
|
|
|
|
Abstract We propose a new concept, two-step degree. Defining it as the capacity of a node of complex networks, we establish a novel capacity--load model of cascading failures of complex networks where the capacity of nodes decreases during the process of cascading failures. For scale-free networks, we find that the average two-step degree increases with the increase of the heterogeneity of the degree distribution, showing that the average two-step degree can be used for measuring the heterogeneity of the degree distribution of complex networks. In addition, under the condition that the average degree of a node is given, we can design a scale-free network with the optimal robustness to random failures by maximizing the average two-step degree.
|
| Keywords:
89.75.Hc
89.75.Fb
|
|
|
Received: 07 March 2008
Published: 26 September 2008
|
|
| PACS: |
89.75.Hc
|
(Networks and genealogical trees)
|
| |
89.75.Fb
|
(Structures and organization in complex systems)
|
|
|
|
|
|
[1] Albert R, Jeong H and Barab\'{asi A L 2000 Nature 406 378
[2] Cohen R, Erez K, ben-Avraham D and Havlin S 2000 Phys. Rev. Lett. 85 4626
[3] Cohen R, Erez K, ben-Avraham D and Havlin S 2001 Phys. Rev. Lett. 86 3682
[4] Callaway D S, Newman M E J, Strogatz S H and Watts D J2000 Phys. Rev. Lett. 85 5468
[5] Gallos L K, Cohen R, Argyrak is P and Havlin S 2005 Phys. Rev. Lett. 94 188701
[6] Shargel B, Sayama H, Epstein I R and Bar-Yam Y 2003 Phys. Rev. Lett. 90 068701
[7] Paul G, Tanizaw A T, Havlin S and Stanley H E 2004 Eur. Phys. J. B 38 187
[8] Valente A X C N, Sarkar A and Stone H A 2004 Phys.Rev. Lett. 92 118702
[9] Tanizawa T, Paul G, Cohen R, Havlin S and Stanley H E 2005 Phys. Rev. E 71 047101
[10] Wang B, Tang H W, Guo C H and Xiu Z L 2006 PhysicaA 363 591
[11] Moreno Y, Gomez J B and Pacheco A. F 2002 Europhys.Lett. 58 630
[12] Motter A E, Nishikawa T and Lai Y C 2002 Phys. Rev.E 66 065102(R)
[13] Newnan M E J, Strogatz S H and Watts D J 2001 Phys.Rev. E 64 026118
[14] Home P and Kim B J 2002 Phys. Rev. E 65056109
[15] Crucitti P,Latora V and Marchiori m 2004 Phys. Rev.E 69 045104
[16] Barab\'{asi A L and Albert R 1999 Science 286509 |
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
