Adopting the initial load of a node j to be Lj = [kj(∑m∈Γjkm)]α with kj and Γj being the degree of the node j and the set of its neighbouring nodes respectively, we propose a cascading model based on a local preferential redistribution rule of the load after removing a node. Assuming that a failed node leads only to a redistribution of the load passing through it to its neighbouring nodes, we explore the response of scale-free networks subject to two different attack strategies on nodes and find some interesting and counterintuitive results in our cascading model. On the one hand, unexpectedly, the attack on the nodes with the lowest degree is more harmful than the attack on the highest degree nodes when α<1/2. On the other hand, when α=1/2, the effects of two attacks for the robustness against cascading failures are almost identical. In addition, the numerical simulations are also verified by the theoretical analysis. These results may be very helpful for real-life networks to protect the key nodes selected effectively and to avoid cascading-failure-induced disasters.
Adopting the initial load of a node j to be Lj = [kj(∑m∈Γjkm)]α with kj and Γj being the degree of the node j and the set of its neighbouring nodes respectively, we propose a cascading model based on a local preferential redistribution rule of the load after removing a node. Assuming that a failed node leads only to a redistribution of the load passing through it to its neighbouring nodes, we explore the response of scale-free networks subject to two different attack strategies on nodes and find some interesting and counterintuitive results in our cascading model. On the one hand, unexpectedly, the attack on the nodes with the lowest degree is more harmful than the attack on the highest degree nodes when α<1/2. On the other hand, when α=1/2, the effects of two attacks for the robustness against cascading failures are almost identical. In addition, the numerical simulations are also verified by the theoretical analysis. These results may be very helpful for real-life networks to protect the key nodes selected effectively and to avoid cascading-failure-induced disasters.
WANG Jian-Wei;RONG Li-Li. Effect Attack on Scale-Free Networks due to Cascading Failures[J]. 中国物理快报, 2008, 25(10): 3826-3829.
WANG Jian-Wei, RONG Li-Li. Effect Attack on Scale-Free Networks due to Cascading Failures. Chin. Phys. Lett., 2008, 25(10): 3826-3829.
[1] Albert R and Barab\'asi A-L 2002 Rev. Mod. Phys. 74 47 [2] Newman M E J 2003 SIAM Rev. 45 167 [3] Zhou T and Wang B H 2004 Chin. Phys. Lett. 221072 [4] Albert R, Jeong H and Barab\'asi A-L 2000 Nature 406 387 [5] Motter A E and Lai Y -C 2002 Phys. Rev. E 66065102(R) [6] Motter A E 2004 Phys. Rev. Lett. 93 098701 [7] Crucitti P et al 2004 Phys. Rev. E 69 045104 [8] Huang L, Yang L and Yang K 2006 Phys. Rev. E 73 036102 [9] Bakke J et al 2006 Europhys. Lett. 76 717 [10] Wang W X and Chen G R 2008 Phys. Rev. E 77026101 [11] Wu Z X et al 2008 Stat. Mech. P05013 [12] Li P et al 2008 Eur. Phys. J. B 62 1 [13] Simonsen I 2005 Physica A 357 317 [14] Olami Z et al 1992 Phys. Rev. Lett. 68 1224 [15] Goh K I et al 2003 Phys. Rev. Lett. 91 148701 [16] Carreras B A et al 2002 Chaos 12 985 [17] Wang X F and Xu J 2004 Phys. Rev. E 70 056113 [18] Barab\'asi A-L and Albert R 1999 Science 286509
2008, Vol. 25 
