Robustness of complex networks is an essential subject for improving their performance when vertices or links are removed due to potential threats. In recent years, significant advancements have been achieved in this field by many researchers. In this paper we show an overview from a novel statistic perspective. We present a brief review about complex networks at first including 2 primary network models, 12 popular attack strategies and the most convincing network robustness metrics. Then, we focus on the correlations of 12 attack strategies with each other, and the difference of the correlations from one network model to the other. We are also curious about the robustness of networks when vertices are removed according to different attack strategies and the difference of robustness from one network model to the other. Our aim is to observe the correlation mechanism of centralities for distinct network models, and compare the network robustness when different centralities are applied as attacking directors to distinct network models. What inspires us is that maybe we can find a paradigm that combines several high-destructive attack strategies to find the optimal strategy based on the deep learning framework.

The application of complex network theory to power grid analysis has been a hot topic in recent years, which mainly manifests itself in four aspects. The first aspect is to model power system networks. The second aspect is to reveal the topology of the grid itself. The third aspect is to reveal the inherent vulnerability and weakness of the power network itself and put forward the pertinent improvement measures to provide guidance for the construction of power grid. The last aspect is to analyze the mechanism of cascading failure and establish the cascading fault model of large power failure. In the past ten years, by using the complex network theory, many researchers have investigated the structural vulnerability of power grids from the point of view of topology. This letter studies the structural vulnerability of power grids according to the effect of selective node removal. We apply several kinds of node centralities including recently-presented second-order centrality (SOC) to guide the node removal attack. We test the effectiveness of all these centralities in guiding the node removal based on several IEEE power grids. Simulation results show that, compared with other node centralities, the SOC is relatively effective in guiding the node removal and can destroy the power grid with negative degree-degree correlation in less steps.

The power grid defines one of the most important technological networks of our times and has been widely studied as a kind of complex network. It has been developed for more than one century and becomes an extremely huge and seemingly robust system. But it becomes extremely fragile as well because some unexpected minimal failures may lead to sudden and massive blackouts. Many works have been carried out to investigate the structural vulnerability of power grids from the topological point of view based on the complex network theory. This Letter focuses on the structural vulnerability of the power grid under the effect of selective node removal. We propose a new kind of node centrality called overall information centrality (OIC) to guide the node removal attack. We test the effectiveness of our centrality in guiding the node removal based on several IEEE power grids. Simulation results show that, compared with other node centralities such as degree centrality (DC), betweenness centrality (BC) and closeness centrality (CC), our OIC is more effective to guide the node removal and can destroy the power grid in less steps.

In this paper, invulnerability and attack strategies are discussed for the undirected unweighted urban road networks and the directed weighted taxi networks of Beijing. Firstly, five new attack strategies, i.e., Initial All Degree (IAD), Initial All Strength (IAS), Recalculated Closeness (RC), Recalculated All Degree (RAD) and Recalculated All Strength (RAS) and five traditional attack strategies, i.e., Initial Degree (ID), Initial Betweenness (IB), Initial Closeness (IC), Recalculated Degree (RD) and Recalculated Betweenness (RB) are adopted to provoke the nodes failure. Secondly, we assess the impacts of these attack strategies using two invulnerability metrics, i.e., S (the relative size of the giant component) and E (the average network efficiency) through simulation experiments by MATLAB. Furthermore, we obtain some conclusions on the basis of the simulation results. Firstly, we discover that IB is more efficient than others for the undirected unweighted 5th ring Beijing road network based on S, and IB is more efficient than others at the beginning while ID is more efficient than IB at last based on E, while IAD causes a greater damage than IAS for the directed weighted 5th ring Beijing taxi network no matter with metrics S or E. Secondly, we find that dynamic attacks are more efficient than their corresponding static attacks, and RB is more destructive than others in all attack graphs while RAD is more destructive than RAS in all attack graphs. Moreover, we propose some suggestions to advance the reliability of the networks according to the simulation results. Additionally, we notice that the damage between ID (RD) and IAD (RAD) is similar due to the large proportion of two-way roads, and we realize that global measures should be employed to estimate the best attack strategy on the basis of that we find the best attack strategy changes with the nodes failure.