VULNERABILITY OF EFFECTIVE ATTACK ON EDGES IN SCALE-FREE NETWORKS DUE TO CASCADING FAILURES

Assume the initial load of an edge ij in a network to be L-ij = [(k(i) Sigma(a is an element of Gamma i) k(a)) (k(j) Sigma(b is an element of Gamma j) k(b))](alpha) with k(i) and k(j) being the degrees of the nodes connected by the edge, where alpha is a tunable parameter which controls the strength of the edge initial load, and Gamma(i) and Gamma(j) are the sets of neighboring nodes of i and j, respectively. We investigate the cascading phenomenon of uncorrelated scale-free networks subject to two different attacking strategies on edges, i.e. attacking on the edges with the highest loads or the lowest loads (LL). By the critical threshold of edge capacity quantifying the network robustness, we numerically discuss the effects of two attacks for the network vulnerability. Interestingly, it is found that the attack on the edge with the LL is highly effective in disrupting the structure of the attacked network when alpha < 0.5. In the case of alpha = 0.5, the effects of two attacks for the network robustness against cascading failures are almost identical. We furthermore provide the theoretical prediction support for the numerical simulations. These results may be very helpful for real-life networks to protect the key edges selected effectively to avoid cascading-failure-induced disasters.