Cascading failures in networks with the harmonic closeness under edge attack strategies

The definition of the edge load is usually confined to the degree and the betweenness. To overcome the limitation, we adopt the harmonic closeness to define the initial load on the edge whose strength is controlled by a tunable parameter θ. It is found that in Barabási-Albert networks (BA networks), Erdos-Renyi networks (ER networks) with θ ≈ 7.6, and Newman-Watts networks(NW networks) with θ ≈ 7, the robustness is the strongest for the different average degrees < k >. We furthermore explore the relationship between the proportion of attacked edges f and the optimal value of θ under the random attack (RA) and the intentional attack (IA). In order to prove the advantage of the harmonic closeness, our method is compared with the definitions concerning the degree, the betweenness of nodes and edges, the PageRank and the communicability angle. Simulation results show that in comparison with other methods, our method leads to less risk of cascading failures regardless of f in artificial and real networks under RA and BA networks under IA. A key finding is that regardless of < k > , the artificial network with our method is more robust than those with other methods. In addition, the failed edge has the less impact on artificial and real networks with the harmonic closeness. These findings may be useful not only for the development of the research on cascading failures, but also for the reasonable distribution of the loads on edges in infrastructure networks.