Cascading Failures in Weighted Networks with the Harmonic Closeness

In order to effectively enhance the robustness of the network against cascading failures, we adopt the harmonic closeness and the information from neighboring nodes through a weight parameter h and an adjustable parameter d to define the node weight. The simulation results show that in artificial networks the optimal value of h increases while the optimal range of d is almost unchanged, as the proportion of attacked nodes f increases. In Barabasi-Albert networks (BA networks), the bigger the value of d is, the smaller the difference of the node weights is, which is opposite to the observation of Newman-Watts networks (NW networks) and Erdos-Renyi networks (ER networks). Moreover, we find that by attacking the node with the lower load, cascading failures more likely take place for a certain value of d, when the value of h or f is smaller. Another key finding is that no matter what the value of f is, BA networks with the harmonic closeness are more robust than the ones with the degree and the betweenness. In NW, ER networks, and the US power grid, the harmonic closeness results in the stronger robustness when the value of f is not small too much. Our work is helpful to design the strategy resisting the occurrence of cascading failures.