Attack structural vulnerability of power grids: A hybrid approach based on complex networks

Power grids have been studied as a typical example of real-world complex networks. Different from previous methods, this paper proposes a hybrid approach for structural vulnerability analysis of power transmission networks, in which a DC power flow model with hidden failures is embedded into the traditional error and attack tolerance methodology to form a new scheme for power grids vulnerability assessment and modeling. The new approach embodies some important characteristics of power transmission networks. Furthermore, the simulation on the standard IEEE 118 bus system demonstrates that a critical region might exist and when the power grid operates in the region, it is vulnerable to both random and intentional attacks. Finally, a brief theoretical analysis is presented to explain the new phenomena.     

An electrical betweenness approach for vulnerability assessment of power grids considering the capacity of generators and load

Most existing research on the vulnerability of power grids based on complex networks ignores the electrical characteristics and the capacity of generators and load. In this paper, the electrical betweenness is defined by considering the maximal demand of load and the capacity of generators in power grids. The loss of load, which reflects the ability of power grids to provide sufficient power to customers, is introduced to measure the vulnerability together with the size of the largest cluster. The simulation results of the IEEE-118 bus system and the Central China Power Grid show that the cumulative distributions of node electrical betweenness follow a power-law and that the nodes with high electrical betweenness play critical roles in both topological structure and power transmission of power grids. The results prove that the model proposed in this paper is effective for analyzing the vulnerability of power grids.     

Do topological models provide good information about electricity infrastructure vulnerability?

In order to identify the extent to which results from topological graph models are useful for modeling vulnerability in electricity infrastructure, we measure the susceptibility of power networks to random failures and directed attacks using three measures of vulnerability: characteristic path lengths, connectivity loss, and blackout sizes. The first two are purely topological metrics. The blackout size calculation results from a model of cascading failure in power networks. Testing the response of 40 areas within the Eastern U.S. power grid and a standard IEEE test case to a variety of attack/failure vectors indicates that directed attacks result in larger failures using all three vulnerability measures, but the attack-vectors that appear to cause the most damage depend on the measure chosen. While the topological metrics and the power grid model show some similar trends, the vulnerability metrics for individual simulations show only a mild correlation. We conclude that evaluating vulnerability in power networks using purely topological metrics can be misleading.     

Weighted complex network analysis of travel routes on the Singapore public transportation system

The structure and properties of public transportation networks have great implications for urban planning, public policies and infectious disease control. We contribute a complex weighted network analysis of travel routes on the Singapore rail and bus transportation systems. We study the two networks using both topological and dynamical analyses. Our results provide additional evidence that a dynamical study adds to the information gained by traditional topological analysis, providing a richer view of complex weighted networks. For example, while initial topological measures showed that the rail network is almost fully connected, dynamical measures highlighted hub nodes that experience disproportionately large traffic. The dynamical assortativity of the bus networks also differed from its topological counterpart. In addition, inspection of the weighted eigenvector centralities highlighted a significant difference in traffic flows for both networks during weekdays and weekends, suggesting the importance of adding a temporal perspective missing from many previous studies.     

Dynamic properties of epidemic spreading on finite size complex networks

The Internet presents a complex topological structure, on which computer viruses can easily spread. By using theoretical analysis and computer simulation methods, the dynamic process of disease spreading on finite size networks with complex topological structure is investigated. On the finite size networks, the spreading process of SIS （susceptibleinfected-susceptible） model is a finite Markov chain with an absorbing state. Two parameters, the survival probability and the conditional infecting probability, are introduced to describe the dynamic properties of disease spreading on finite size networks. Our results can help understanding computer virus epidemics and other spreading phenomena on communication and social networks. Also, knowledge about the dynamic character of virus spreading is helpful for adopting immunity policy.     

Vulnerability of labeled networks

We propose a metric for vulnerability of labeled graphs that has the following two properties: (1) when the labeled graph is considered as an unlabeled one, the metric reduces to the corresponding metric for an unlabeled graph; and (2) the metric has the same value for differently labeled fully connected graphs, reflecting the notion that any arbitrarily labeled fully connected topology is equally vulnerable as any other. A vulnerability analysis of two real-world networks, the power grid of the European Union, and an autonomous system network, has been performed. The networks have been treated as graphs with node labels. The analysis consists of calculating characteristic path lengths between labels of nodes and determining largest connected cluster size under two node and edge attack strategies. Results obtained are more informative of the networks’ vulnerability compared to the case when the networks are modeled with unlabeled graphs.     

A Path-Based Distribution Measure for Network Comparison

As network data increases, it is more common than ever for researchers to analyze a set of networks rather than a single network and measure the difference between networks by developing a number of network comparison methods. Network comparison is able to quantify dissimilarity between networks by comparing the structural topological difference of networks. Here, we propose a kind of measures for network comparison based on the shortest path distribution combined with node centrality, capturing the global topological difference with local features. Based on the characterized path distributions, we define and compare network distance between networks to measure how dissimilar the two networks are, and the network entropy to characterize a typical network system. We find that the network distance is able to discriminate networks generated by different models. Combining more information on end nodes along a path can further amplify the dissimilarity of networks. The network entropy is able to detect tipping points in the evolution of synthetic networks. Extensive numerical simulations reveal the effectivity of the proposed measure in network reduction of multilayer networks, and identification of typical system states in temporal networks as well.     

Toward cell circuitry: Topological analysis of enzyme reaction networks via reaction route graphs

The first step toward developing complete cell circuitry is to build quantitative networks for enzyme reactions. The conventional King-Altman-Hill (KAH) algorithm for topological analysis of enzyme networks, adapted from electrical networks, is based on “Reaction Graphs” that, unlike electrical circuits, are not quantitative, being straightforward renderings of conventional schematics of reaction mechanisms. Therefore, we propose the use of “Reaction Route (RR) Graphs” instead, as a more suitable graph-theoretical representation for topological analysis of enzyme reaction networks. The RR Graphs are drawn such that they are not only useful for visualizing the various reaction routes or pathways, but unlike Reaction Graphs possess network properties consistent with requisite kinetic, mass balance, and thermodynamic constraints. Therefore, they are better than the conventional Reaction Graphs for topological representation and analysis of enzyme reactions, both via the KAH methodology as well as via numerical matrix inversion. The difference between the two is highlighted based on the example of a single enzyme reaction network for the conversion of 7,8-dihydrofolate and NADPH into 5,6,7,8-tetrahydrofolate and NADP⁺, catalyzed by the enzyme dihydrofolate reductase.     

利用邻域“结构洞”寻找社会网络中最具影响力节点

识别复杂网络中的关键节点对网络结构优化和鲁棒性增强具有十分重要的意义. 经典的关键节点测量方法在一定程度上能够辨识网络中影响力节点, 但存在一定局限性: 局部中心性测量方法仅考虑节点邻居的数目, 忽略了邻居间的拓扑关系, 不能在计算中反映邻居节点间的相互作用; 全局测量方法则由于算法本身的复杂性而不能应用于大规模社会网络的分析, 另外, 经典的关键节点测量方法也没有考虑社会网络特有的社区特征. 为高效、准确地辨识具有社区结构的社会网络中最具影响力节点, 提出了一种基于节点及其邻域结构洞的局部中心性测量方法, 该方法综合考虑了节点的邻居数量及其与邻居间的拓扑结构, 在节点约束系数的计算中同时体现了节点的度属性和“桥接”属性. 利用SIR(易感-感染-免疫)模型在真实社会网络数据上对节点传播能力进行评价后发现, 所提方法可以准确地评价节点的传播能力且具有强的鲁棒性.     

Planar unclustered scale-free graphs as models for technological and biological networks

Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases — usually associated with topological restrictions — their clustering is low and they are almost planar. In this paper we introduce a family of graphs which share all these properties and are defined by two parameters. As their construction is deterministic, we obtain exact analytic expressions for relevant properties of the graphs including the degree distribution, degree correlation, diameter, and average distance, as a function of the two defining parameters. Thus, the graphs are useful to model some complex networks, in particular several families of technological and biological networks, and in the design of new practical communication algorithms in relation to their dynamical processes. They can also help understanding the underlying mechanisms that have produced their particular structure.     

Deterministic weighted scale-free small-world networks

We propose a deterministic weighted scale-free small-world model for considering pseudofractal web with the co-evolution of topology and weight. Considering the fluctuations in traffic flow constitute a main reason for congestion of packet delivery and poor performance of communication networks, we suggest a recursive algorithm to generate the network, which restricts the traffic fluctuations on it effectively during the evolutionary process. We provide a relatively complete view of topological structure and weight dynamics characteristics of the networks such as weight and strength distribution, degree correlations, average clustering coefficient and degree-cluster correlations as well as the diameter.     

Social power and opinion formation in complex networks

In this paper we investigate the effects of social power on the evolution of opinions in model networks as well as in a number of real social networks. A continuous opinion formation model is considered and the analysis is performed through numerical simulation. Social power is given to a proportion of agents selected either randomly or based on their degrees. As artificial network structures, we consider scale-free networks constructed through preferential attachment and Watts–Strogatz networks. Numerical simulations show that scale-free networks with degree-based social power on the hub nodes have an optimal case where the largest number of the nodes reaches a consensus. However, given power to a random selection of nodes could not improve consensus properties. Introducing social power in Watts–Strogatz networks could not significantly change the consensus profile.     

一个描述合作网络顶点度分布的模型

讨论一类社会合作网络以及一些与其拓扑结构相似的技术网络的度分布.建议一个最简化模型，通过解析的方法说明这些网络演化的共同动力学机理，而且说明顶点的度分布和项目度分布之间具有密切的一致关系，而项目所含的顶点数分布对度分布的影响较小；对模型的更一般情况进行数值模拟，说明上述结论具有一定的普遍性.这个模型显示这类广义的合作网络一般具有处于幂函数和指数函数这两种极端情况之间的度分布.简要介绍对一些实际合作网络做统计研究的结果，说明本模型的合理性. 关键词： 合作网络 度分布 项目度分布 项目含顶点数     

Optimization-based structure identification of dynamical networks

The topological structure of a dynamical network plays a pivotal part in its properties, dynamics and control. Thus, understanding and modeling the structure of a network will lead to a better knowledge of its evolutionary mechanisms and to a better cottoning on its dynamical and functional behaviors. However, in many practical situations, the topological structure of a dynamical network is usually unknown or uncertain. Thus, exploring the underlying topological structure of a dynamical network is of great value. In recent years, there has been a growing interest in structure identification of dynamical networks. As a result, various methods for identifying the network structure have been proposed. However, in most of the previous work, few of them were discussed in the perspective of optimization. In this paper, an optimization algorithm based on the projected conjugate gradient method is proposed to identify a network structure. It is straightforward and applicable to networks with or without observation noise. Furthermore, the proposed algorithm is applicable to dynamical networks with partially observed component variables for each multidimensional node, as well as small-scale networks with time-varying structures. Numerical experiments are conducted to illustrate the good performance and universality of the new algorithm.     

Topology and dynamics of attractor neural networks: The role of loopiness

We derive an exact representation of the topological effect on the dynamics of sequence processing neural networks within signal-to-noise analysis. A new network structure parameter, loopiness coefficient, is introduced to quantitatively study the loop effect on network dynamics. A large loopiness coefficient means a high probability of finding loops in the networks. We develop recursive equations for the overlap parameters of neural networks in terms of their loopiness. It was found that a large loopiness increases the correlation among the network states at different times and eventually reduces the performance of neural networks. The theory is applied to several network topological structures, including fully-connected, densely-connected random, densely-connected regular and densely-connected small-world, where encouraging results are obtained.     

Impact of core-periphery structure on cascading failures in interdependent scale-free networks

Core-periphery structure is a typical meso-scale structure in networks. Previous studies on core-periphery structure mainly focus on the improvement of detection methods, while the research on the impact of core-periphery structure on cascading failures in interdependent networks is still missing. Therefore, we investigate the cascading failures of interdependent scale-free networks with different core-periphery structures and coupling preferences in the paper. First, we introduce an evaluation index to calculate the goodness of core-periphery structure. Second, we propose a new scale-free network evolution model, which can generate tunable core-periphery structures, and its degree distribution is analyzed mathematically. Finally, based on a degree-load-based cascading failure model, we mainly investigate the impact of goodness of core-periphery structure on cascading failures in both symmetrical and asymmetrical interdependent networks. Through numerical simulations, we find that with the same average degree, the networks with weak core-periphery structure will be more robust, while the initial load on node will influence the improvement of robustness. In addition, we also find that the inter-similarity coupling performs better than random coupling. These findings may be helpful for building resilient interdependent networks.     

Link prediction in complex networks via modularity-based belief propagation

Link prediction aims at detecting missing, spurious or evolving links in a network, based on the topological information and/or nodes' attributes of the network. Under the assumption that the likelihood of the existence of a link between two nodes can be captured by nodes' similarity, several methods have been proposed to compute similarity directly or indirectly, with information on node degree. However, correctly predicting links is also crucial in revealing the link formation mechanisms and thus in providing more accurate modeling for networks. We here propose a novel method to predict links by incorporating stochastic-block-model link generating mechanisms with node degree. The proposed method first recovers the underlying block structure of a network by modularity-based belief propagation, and based on the recovered block structural information it models the link likelihood between two nodes to match the degree sequence of the network. Experiments on a set of real-world networks and synthetic networks generated by stochastic block model show that our proposed method is effective in detecting missing, spurious or evolving links of networks that can be well modeled by a stochastic block model. This approach efficiently complements the toolbox for complex network analysis, offering a novel tool to model links in stochastic block model networks that are fundamental in the modeling of real world complex networks.     

Surveying network community structure in the hidden metric space

Most real-world networks from various fields share a universal topological property as community structure. In this paper, we propose a node-similarity based mechanism to explore the formation of modular networks by applying the concept of hidden metric spaces of complex networks. It is demonstrated that network community structure could be formed according to node similarity in the underlying hidden metric space. To clarify this, we generate a set of observed networks using a typical kind of hidden metric space model. By detecting and analyzing corresponding communities both in the observed network and the hidden space, we show that the values of the fitness are rather close, and the assignments of nodes for these two kinds of community structures detected based on the fitness parameter are extremely matching ones. Furthermore, our research also shows that networks with strong clustering tend to display prominent community structures with large values of network modularity and fitness.     

Semantic networks based on titles of scientific papers

In this paper we study the topological structure of semantic networks based on titles of papers published in scientific journals. It discusses its properties and presents some reflections on how the use of social and complex network models can contribute to the diffusion of knowledge. The proposed method presented here is applied to scientific journals where the titles of papers are in English or in Portuguese. We show that the topology of studied semantic networks are small-world and scale-free.     

基于移动社交网络的谣言传播动力学研究

本文在CSR传播模型的基础上提出基于移动社交网络的CSR的谣言传播模型. 改进了CSR模型的传播规则和传播动力学方程, 使得更符合移动SNS上用户的使用习惯. 在CSR模型中的接受概率数学模型基础上, 考虑个人接受阈值对接受概率的影响, 更符合人类接受谣言的心理学特点. 本文对该传播模型进行了理论分析. 并在仿真实验中, 利用多agent仿真平台对新模型和CSR模型以及SIR模型 在匀质网络和异质网络中的传播效果进行了对比研究, 从实验的结果来看, 新的谣言传播模型在匀质网络中传播范围更广, 传播速度更快. 新模型具有初值敏感性的特点. 关键词： 复杂网络 移动社交网络 谣言传播