Exploring the robustness of urban bus network: A case from Southern China

The robustness of urban bus network is essential to a city that heavily relies on buses as its main transportation solution. In this paper, the urban bus network has been modeled as a directed and space L network, and Changsha, a transportation hub of nearly 8 million people and hundreds of bus lines in southern China, is taken as a case. Based on the quantitative analyses of the topological properties, it is found that Changsha urban bus network is a scale-free network, not a small-world network. To evaluate the robustness of the network, five scenarios of network failure are simulated, including a random failure and four types of intentional attacks that differed in key node identification methods (i.e., unweighted degree or betweenness centrality) and attack strategies (i.e., normal or cascading attack). It is revealed that intentional attacks are more destructive than a random failure, and cascading attacks are more disruptive than normal attacks in the urban bus network. In addition, the key nodes identification methods are found to play a critical role in the robustness of the urban bus network. Specifically, cascading attack could be more disruptive when the betweenness centrality is used to identify key nodes; in contrast, normal attack could be more disruptive when the unweighted degree is used to identify key nodes. Our results could provide reference for risk management of urban bus network.     

Two-peak and three-peak optimal complex networks

A central issue in complex networks is tolerance of random failures and intentional attacks. Current literature emphasizes the dichotomy between networks with a power-law node connectivity distribution, which are robust to random failures but fragile to targeted attacks, versus networks with an exponentially decaying connectivity distribution, which are less tolerant to failures but more resilient to attacks. We prove analytically that the optimal network configuration under a classic measure of robustness is altogether different from both of the above: in all cases, failure and/or attack, there are no more than three distinct node connectivities in the optimal network.     

Topological Properties of Urban Public Traffic Networks in Chinese Top-Ten Biggest Cities

We investigate the topological characteristics of complex networks as exemplified by the urban public traffic network （UPTN） in Chinese top-ten biggest cities. It is found that the UPTNs have small world behaviour, by the examination of their topological parameters. The quantitative analysis of the transport efficiency of the UPTNs reveals their higher local efficiency El and lower global efficiency Eg, which coincide well with the status quo of those Chinese cities still at their developing stage. Furthermore, the topological properties of efficiency in the UPTNs are also examined, and the findings indicate that, on the one hand, the UPTNs show robustness to random attacks and frangibility to malicious attacks on a global scale; on the other hand, the interrelation between UPTN efficiency and network motifs deserves our attention. The motifs which interrelate the UPTN efficiency are always triangular-formed patterns, e.g. motifs ID 238, ID 174 and ID 102, etc.     

Error and attack tolerance of evolving networks with local preferential attachment

Networks generated by local-world evolving network model display a transition from exponential network to power-law network with respect to connectivity distribution. We investigate statistical properties of the evolving networks and the responses of these networks under random errors and intentional attacks. It has been found that local world size M has great effect on the network's heterogeneity, thus leading to transitional behaviors in network's robustness against errors and attacks. Numerical results show that networks constructed with local preferential attachment mechanism can maintain the robustness of scale-free networks under random errors and concurrently improve reliance against targeted attacks on highly connected nodes.     

一种全局同质化相依网络耦合模式

相依网络的相依模式(耦合模式)是影响其鲁棒性的重要因素之一.本文针对具有无标度特性的两个子网络提出一种全局同质化相依网络耦合模式.该模式以子网络的总度分布均匀化为原则建立相依网络的相依边,一方面压缩度分布宽度,提高其对随机失效的抗毁性,另一方面避开对度大节点(关键节点)的相依,提高其对蓄意攻击的抗毁性.论文将其与常见的节点一对一的同配、异配及随机相依模式以及一对多随机相依模式作了对比分析,仿真研究其在随机失效和蓄意攻击下的鲁棒性能.研究结果表明,本文所提全局同质化相依网络耦合模式能大大提高无标度子网络所构成的相依网络抗级联失效能力.本文研究成果能够为相依网络的安全设计等提供指导意义.     

基于有限资源提升网络可生存性的拓扑重构方法

给定网络拓扑结构和有限添加边资源,如何优化配置添加边使重构后的网络拓扑结构具有最优可生存性是非常有价值的研究问题.本文首先明确网络可生存性的量化评估指标,以移除节点后网络结构的鲁棒性和有效性为优化目标,提出网络拓扑重构优化问题的建模与分析方法.同时在给定资源代价的约束下,为实现添加边资源配置效率的最大化,提出优先配置节点加强保护圈的启发式算法.仿真实验表明,该算法在有限资源约束的随机局部故障和选择性攻击环境中,能兼顾改善网络鲁棒性和传输效率,有效提升网络结构的可生存性.     

Exploring evolutionary features of directed weighted hazard network in the subway construction

A better understanding of previous accidents is an effective way to reduce the occurrence of similar accidents in the future. In this paper, a complex network approach is adopted to construct a directed weighted hazard network(DWHN) to analyze topological features and evolution of accidents in the subway construction. The nodes are hazards and accidents, the edges are multiple relationships of these nodes and the weight of edges are occurrence times of repetitive relationships. The results indicate that the DWHN possesses the property of small-world with small average path length and large clustering coefficient, indicating that hazards have better connectivity and will spread widely and quickly in the network. Moreover,the DWHN has the property of scale-free network for the cumulative degree distribution follows a power-law distribution.It makes DWHN more vulnerable to target attacks. Controlling key nodes with higher degree, strength and betweenness centrality will destroy the connectivity of DWHN and mitigate the spreading of accidents in the network. This study is helpful for discovering inner relationships and evolutionary features of hazards and accidents in the subway construction.     

False Positive and False Negative Effects on Network Attacks

Robustness against attacks serves as evidence for complex network structures and failure mechanisms that lie behind them. Most often, due to detection capability limitation or good disguises, attacks on networks are subject to false positives and false negatives, meaning that functional nodes may be falsely regarded as compromised by the attacker and vice versa. In this work, we initiate a study of false positive/negative effects on network robustness against three fundamental types of attack strategies, namely, random attacks (RA), localized attacks (LA), and targeted attack (TA). By developing a general mathematical framework based upon the percolation model, we investigate analytically and by numerical simulations of attack robustness with false positive/negative rate (FPR/FNR) on three benchmark models including Erd?s-Rényi (ER) networks, random regular (RR) networks, and scale-free (SF) networks. We show that ER networks are equivalently robust against RA and LA only when FPR equals zero or the initial network is intact. We find several interesting crossovers in RR and SF networks when FPR is taken into consideration. By defining the cost of attack, we observe diminishing marginal attack efficiency for RA, LA, and TA. Our finding highlights the potential risk of underestimating or ignoring FPR in understanding attack robustness. The results may provide insights into ways of enhancing robustness of network architecture and improve the level of protection of critical infrastructures.     

Optimization of robustness and connectivity in complex networks

Scale-free networks rely on a relatively small number of highly connected nodes to achieve a high degree of interconnectivity and robustness to random failure, but suffer from a high sensitivity to directed attack. In this paper we describe a parameterized family of networks and analyze their connectivity and sensitivity, identifying a network that has an interconnectedness closer to that of a scale-free network, a robustness to attack closer to that of an exponential network, and a resistance to failure better than that of either of those networks.     

A Robustness Model of Complex Networks with Tunable Attack Information Parameter

We introduce a novel model for robustness of complex with a tunable attack information parameter. The random failure and intentional attack known are the two extreme cases of our model. Based on the model, we study the robustness of complex networks under random information and preferential information, respectively. Using the generating function method, we derive the exact value of the critical removal fraction of nodes for the disintegration of networks and the size of the giant component. We show that hiding just a small fraction of nodes randomly can prevent a scale-free network from collapsing and detecting just a small fraction of nodes preferentially can destroy a scale-free network.     

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.     

基于感知流量算法的复杂网络拥塞问题研究

研究了在具有感知流量的路由策略下,复杂网络的拓扑结构对网络中传输流量的影响.为了描述数据包传输过程的有效性,通过引入一个状态参数,利用由稳态到拥塞的指标流量相变值来刻画网络的吞吐量.基于每个节点的数据包处理能力与该节点的度或介数成比例提出两种模型并进行仿真.仿真结果表明,平均度相同的情况下,模型Ⅰ中,WS小世界网络比ER随机网络和BA无标度网络更容易产生拥塞;模型Ⅱ中,所有网络容量都得到较大的提高,尤其是WS小世界网络.但当网络的基本连接参数改变时,哪种模型更利于网络的流量传输,还要依据网络本身的结构特性 关键词： 复杂网络 无标度网络 感知流量 拥塞     

Properties of Bottleneck on Complex Networks

The traffic bottleneck plays a key role in most of the natural and artificial network. Here we present a simply model for bottleneck dynamical characteristics consideration the reliability on the complex network by taking into account the network topology characteristics and system size. We find that there is a critical rate of flow generation below which the network traffic is free but above which traffic congestion occurs. Also, it is found that random networks have larger critical flow generating rate than scale free ones. Analytical results may be practically useful for designing networks, especially for the urban traffic network.     

Emergent criticality through adaptive information processing in boolean networks

We study information processing in populations of boolean networks with evolving connectivity and systematically explore the interplay between the learning capability, robustness, the network topology, and the task complexity. We solve a long-standing open question and find computationally that, for large system sizes N, adaptive information processing drives the networks to a critical connectivity K(c)=2. For finite size networks, the connectivity approaches the critical value with a power law of the system size N. We show that network learning and generalization are optimized near criticality, given that the task complexity and the amount of information provided surpass threshold values. Both random and evolved networks exhibit maximal topological diversity near K(c). We hypothesize that this diversity supports efficient exploration and robustness of solutions. Also reflected in our observation is that the variance of the fitness values is maximal in critical network populations. Finally, we discuss implications of our results for determining the optimal topology of adaptive dynamical networks that solve computational tasks.     

基于复杂网络理论的多元混合空管技术保障系统网络特征分析

为提高空管技术保障系统应对突发事件的能力,本文以空管技术保障系统导航、通信、监视设备覆盖的航路结构为基础,构建系统对应的空间网络模型.提出从灵活性、鲁棒性、高效性三个方面度量空管技术保障系统网络特性,对北京、上海、广州、昆明、沈阳、兰州飞行情报区的空管技术保障系统网络的平均度、度分布、度-度相关性、聚集系数、平均路径长度、直径等进行分析.分析结果显示,各飞行情报区空管技术保障系统的平均聚集系数在0.25—0.39之间,网络聚集程度偏低;网络平均路径长度为3.4,表现出小世界网络特征;度值3时服从幂律分布,度-度分布不表现出正相关或负相关.对网络进行基于度优先的和随机的抗毁性测度,空管技术保障系统网络抗毁性较差,网络的可靠性由少数核心节点决定,应对核心节点进行目标免疫,提高网络的抗毁性.这些规律为空管技术保障系统能力提升、新建扩建提供理论依据,对降低突发事件对空管系统保障能力的影响,保障空中交通持续安全具有现实意义.     

Optimal traffic networks topology: A complex networks perspective

We investigate and analyse an optimal traffic network structure for resisting traffic congestion with different volumes of traffic. For this aim, we introduce a cost function and user-equilibrium assignment (UE) which ensures the flow balance on traffic systems. Our finding is that an optimal network is strongly dependent on the total system flow. And the random network is most desirable when the system flow is small. But for the larger volume of traffic, the network with power-law degree distribution is the optimal one. Further study indicates, for scale-free networks, that the degree distribution exponent has large effects on the congestion of traffic network. Therefore, the volume of traffic and characteristic of network determine the optimal network structure so as to minimize the side-effect produced by traffic congestion.     

地铁站内交织行人流的简化模型和数值模拟

地铁站内多方向行人流以不同方式通过瓶颈时具有不同的效率,发生拥堵的机制也有所不同. 本文将地铁站内行人流的交织运动简化为连通双通道内两股行人通过瓶颈的情形. 采用推广的格子气模型,通过引入背景场,使改进的模型可以刻画地铁站内行人流的运动特征, 通过数值模拟研究了两股行人以两种不同方式经过研究区域的清空时间以及瓶颈宽度的影响. 研究发现,在模型中考虑行人沿对角线的运动可以更加准确地描述真实行人运动. 当瓶颈宽度小于临界宽度时,逆向交织的行人经过研究区域具有更高的效率, 验证了行人流实验的结果.此外还详细讨论了在瓶颈处发生拥堵的机理.     

Enhancement of scale-free network attack tolerance

Despite the large size of most communication and transportation systems,there are short paths between nodes in these networks which guarantee the efficient information,data and passenger delivery;furthermore these networks have a surprising tolerance under random errors thanks to their inherent scale-free topology.However,their scale-free topology also makes them fragile under intentional attacks,leaving us a challenge on how to improve the network robustness against intentional attacks without losing their strong tolerance under random errors and high message and passenger delivering capacity.Here we propose two methods (SL method and SH method) to enhance scale-free network’s tolerance under attack in different conditions.     

Authenticated Quantum Key Distribution with Collective Detection using Single Photons

We present two authenticated quantum key distribution (AQKD) protocols by utilizing the idea of collective (eavesdropping) detection. One is a two-party AQKD protocol, the other is a multiparty AQKD protocol with star network topology. In these protocols, the classical channels need not be assumed to be authenticated and the single photons are used as the quantum information carriers. To achieve mutual identity authentication and establish a random key in each of the proposed protocols, only one participant should be capable of preparing and measuring single photons, and the main quantum ability that the rest of the participants should have is just performing certain unitary operations. Security analysis shows that these protocols are free from various kinds of attacks, especially the impersonation attack and the man-in-the-middle (MITM) attack.     

A network analysis of the Chinese stock market

In many practical important cases, a massive dataset can be represented as a very large network with certain attributes associated with its vertices and edges. Stock markets generate huge amounts of data, which can be use for constructing the network reflecting the market’s behavior. In this paper, we use a threshold method to construct China’s stock correlation network and then study the network’s structural properties and topological stability. We conduct a statistical analysis of this network and show that it follows a power-law model. We also detect components, cliques and independent sets in this network. These analyses allows one to apply a new data mining technique of classifying financial instruments based on stock price data, which provides a deeper insight into the internal structure of the stock market. Moreover, we test the topological stability of this network and find that it displays a topological robustness against random vertex failures, but it is also fragile to intentional attacks. Such a network stability property would be also useful for portfolio investment and risk management.