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.

Many important problems in communication networks, transportation networks, and logistics networks are solved by the minimization of cost functions. In general, these can be complex optimization problems involving many variables. However, physicists noted that in a network, a node variable (such as the amount of resources of the nodes) is connected to a set of link variables (such as the flow connecting the node), and similarly each link variable is connected to a number of (usually two) node variables. This enables one to break the problem into local components, often arriving at distributive algorithms to solve the problems. Compared with centralized algorithms, distributed algorithms have the advantages of lower computational complexity, and lower communication overhead. Since they have a faster response to local changes of the environment, they are especially useful for networks with evolving conditions. This review will cover message-passing algorithms in applications such as resource allocation, transportation networks, facility location, traffic routing, and stability of power grids.

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.

The controllability of complex networks has attracted increasing attention within various scientific fields. Many power grids are complex networks with some common topological characteristics such as small-world and scale-free features. This Letter investigate the controllability of some real power grids in comparison with classical complex network models with the same number of nodes. Several conclusions are drawn after detailed analyses using several real power grids together with Erdös-Rényi (ER) random networks, Wattz-Strogatz (WS) small-world networks, Barabási-Albert (BA) scale-free networks and configuration model (CM) networks. The main conclusion is that most driver nodes of power grids are hub-free nodes with low nodal degree values of 1 or 2. The controllability of power grids is determined by degree distribution and heterogeneity, and power grids are harder to control than WS networks and CM networks while easier than BA networks. Some power grids are relatively difficult to control because they require a far higher ratio of driver nodes than ER networks, while other power grids are easier to control for they require a driver node ratio less than or equal to ER random networks.