相依网络的条件依赖群逾渗

相依网络鲁棒性研究多集中于满足无反馈条件的一对一依赖,但现实网络节点往往依赖于多节点构成的依赖群,即使群内部分节点失效也不会导致依赖节点失效.针对此现象提出了一种相依网络的条件依赖群逾渗模型,该模型允许依赖群内节点失效比例不超过容忍度γ时,依赖节点仍可正常工作.通过理论分析给出了基于生成函数方法的模型巨分量方程,仿真结果表明方程理论解与相依网络模拟逾渗值相吻合,增大γ值和依赖群规模可提高相依网络鲁棒性.本文模型有助于更好地理解现实网络逾渗现象,对如何增强相依网络鲁棒性有一定指导作用.     

多层网络级联失效的预防和恢复策略概述

现实生活中,与国计民生密切相关的基础设施网络大多不是独立存在的,而是彼此之间相互联系或依赖的,于是用于研究这些系统的多层网络模型随之产生.多层网络中的节点在失效或者遭受攻击后会因"层内"和"层间"的相互作用而产生级联效应,从而使得失效能够在网络层内和层间反复传播并使得失效规模逐步放大.因此,多层网络比单个网络更加脆弱.多层网络级联失效产生的影响和损失往往是非常巨大的,所以对多层网络级联失效的预防和恢复的研究具有重大意义.就多层网络级联失效的预防而言,主要包含故障检测,保护重要节点,改变网络耦合机制和节点备份等策略.就多层网络发生级联失效后的恢复策略而言,主要包含共同边界节点恢复、空闲连边恢复、加边恢复、重要节点优先恢复、更改拓扑结构、局域攻击修复、自适应边修复等策略.     

相依网络上基于相连边的择优恢复算法

如何有效地应对和控制故障在相依网络上的级联扩散避免系统发生结构性破碎,对于相依网络抗毁性研究具有十分重要的理论价值和现实意义.最新的研究提出一种基于相依网络的恢复模型,该模型的基本思想是通过定义共同边界节点,在每轮恢复阶段找出符合条件的共同边界节点并以一定比例实施恢复.当前的做法是按照随机概率进行选择.这种方法虽然简单直观,却没有考虑现实世界中资源成本的有限性和择优恢复的必然性.为此,针对相依网络的恢复模型,本文利用共同边界节点在极大连通网络内外的连接边数计算边界节点的重要性,提出一种基于相连边的择优恢复算法(preferential recovery based on connectivity link,PRCL)算法.利用渗流理论的随机故障模型,通过ER随机网络和无标度网络构建的不同结构相依网络上的级联仿真结果表明,相比随机方法和度数优先以及局域影响力优先的恢复算法,PRCL算法具备恢复能力强、起效时间早且迭代步数少的优势,能够更有效、更及时地遏制故障在网络间的级联扩散,极大地提高了相依网络遭受随机故障时的恢复能力.     

基于相继故障信息的网络节点重要度演化机理分析

分析了过载机制下节点重要度的演化机理.首先,在可调负载重分配级联失效模型基础上,根据节点失效后其分配范围内节点的负载振荡程度,提出了考虑级联失效局域信息的复杂网络节点重要度指标.该指标具有两个特点:一是值的大小可以清晰地指出节点的失效后果;二是可以依据网络负载分配范围、负载分配均匀性、节点容量系数及网络结构特征分析节点重要度的演化情况.然后,给出该指标的仿真算法,并推导了最近邻择优分配和全局择优分配规则下随机网络和无标度网络节点重要度的解析表达式.最后,实验验证了该指标的有效性和可行性,并深入分析了网络中节点重要度的演化机理,即非关键节点如何演化成影响网络级联失效行为的关键节点.     

带有层级结构的复杂网络级联失效模型

针对现实世界的网络中普遍存在的层级结构建立一个级联失效模型, 该模型可用于优化金融、物流网络设计. 选择的层级网络模型具有树形骨架和异质的隐含连接, 并且骨架中每层节点拥有的分枝数服从正态分布. 级联失效模型中对底层节点的打击在不完全信息条件下进行, 也即假设打击者无法观察到隐含连接. 失效节点的负载重分配考虑了层级异质性, 它可以选择倾向于向同级或高层级完好节点分配额外负载. 仿真实验表明, 层级网络的拓扑结构随连接参数变化逐渐从小世界网络过渡到随机网络. 网络级联失效规模随隐含连接比例呈现出先增加后降低的规律. 负载重分配越倾向于高层级节点, 网络的抗毁损性越高. 同时, 由于连接参数会改变隐含连接在不同层级之间的分布, 进而对网络的抗毁损性产生显著影响, 为了提高网络抗毁损能力, 设计网络、制定管理控制策略时应合理设定连接参数. 关键词： 复杂网络 级联失效 层级结构     

Complex networks: Dynamics and security

This paper presents a perspective in the study of complex networks by focusing on how dynamics may affect network security under attacks. In particular, we review two related problems: attack-induced cascading breakdown and range-based attacks on links. A cascade in a network means the failure of a substantial fraction of the entire network in a cascading manner, which can be induced by the failure of or attacks on only a few nodes. These have been reported for the internet and for the power grid (e.g., the August 10, 1996 failure of the western United States power grid). We study a mechanism for cascades in complex networks by constructing a model incorporating the flows of information and physical quantities in the network. Using this model we can also show that the cascading phenomenon can be understood as a phase transition in terms of the key parameter characterizing the node capacity. For a parameter value below the phase-transition point, cascading failures can cause the network to disintegrate almost entirely. We will show how to obtain a theoretical estimate for the phase-transition point. The second problem is motivated by the fact that most existing works on the security of complex networks consider attacks on nodes rather than on links. We address attacks on links. Our investigation leads to the finding that many scale-free networks are more sensitive to attacks on short-range than on long-range links. Considering that the small-world phenomenon in complex networks has been identified as being due to the presence of long-range links, i.e., links connecting nodes that would otherwise be separated by a long node-to-node distance, our result, besides its importance concerning network efficiency and security, has the striking implication that the small-world property of scale-free networks is mainly due to short-range links.     

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.     

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.     

基于超图的超网络相继故障分析

分析了快递超网络和电子元件超网络的相继故障扩散方式, 结合超图理论提出了2-section 图分析法和线图分析法, 并仿真分析了无标度超网络耦合映像格子的相继故障进程. 结果表明: 无标度超网络对外部攻击表现出了既鲁棒又脆弱的特性. 针对相继故障的不同扩散方式, 无标度超网络的相继故障行为表现出不同的特点. 超网络的相继故障行为和超网络的超度以及超边度分布有密切的联系, 也和超网络中超边的个数有关. 通过和同规模的Barabasi-Albert (BA)无标度网络对比, 在同一种攻击方式下同规模的无标度超网络都比BA 无标度网络表现出了更强的鲁棒性. 另外, 基于超边扩散的相继故障进程比基于节点扩散的相继故障进程更加缓慢.     

Robustness of Cyber-Physical Supply Networks in Cascading Failures

A cyber-physical supply network is composed of an undirected cyber supply network and a directed physical supply network. Such interdependence among firms increases efficiency but creates more vulnerabilities. The adverse effects of any failure can be amplified and propagated throughout the network. This paper aimed at investigating the robustness of the cyber-physical supply network against cascading failures. Considering that the cascading failure is triggered by overloading in the cyber supply network and is provoked by underload in the physical supply network, a realistic cascading model for cyber-physical supply networks is proposed. We conducted a numerical simulation under cyber node and physical node failure with varying parameters. The simulation results demonstrated that there are critical thresholds for both firm’s capacities, which can determine whether capacity expansion is helpful; there is also a cascade window for network load distribution, which can determine the cascading failures occurrence and scale. Our work may be beneficial for developing cascade control and defense strategies in cyber-physical supply networks.     

Phase Transition in Recovery Process of Complex Networks

The dynamic characteristic of complex network failure and recovery is one of the main research topics in complex networks. Real world systems such as traffic jams and Internet recovery could be described by the complex network theory. We propose a model to study the recovery process in complex networks. Two different recovery mechanisms are considered in three kinds of networks: external recovery and internal recovery. By simulating the process of the nodes recovery in networks, it is found that the system exhibits the feature of first-order phase transition only when the external recovery is considered. Internal recovery cannot induce such a kind of transitions. As external recovery and internal recovery coexist on networks, the systems will retain the most efficient part of external recovery and internal recovery. Meanwhile, a hysteresis could be observed when increasing or decreasing the failure probability. Finally; a largest degree node protection strategy is proposed for improving the robustness of networks.     

Cascading Failures of Complex Networks Based on Two-Step Degree

We propose a new concept, two-step degree. Defining it as the capacity of a node of complex networks, we establish a novel capacity-load model of cascading failures of complex networks where the capacity of nodes decreases during the process of cascading failures. For scale-free networks, we find that the average two-step degree increases with the increase of the heterogeneity of the degree distribution, showing that the average two- step degree can be used for measuring the heterogeneity of the degree distribution of complex networks. In addition, under the condition that the average degree of a node is given, we can design a scale-free network with the optimal robustness to random failures by maximizing the average two-step degree.     

An LCOR model for suppressing cascading failure in weighted complex networks

Based on the relationship between capacity and load, cascading failure on weighted complex networks is investigated, and a load-capacity optimal relationship (LCOR) model is proposed in this paper. Compared with three other kinds of load-capacity linear or non-linear relationship models in model networks as well as a number of real-world weighted networks including the railway network, the airports network and the metro network, the LCOR model is shown to have the best robustness against cascading failure with less cost. Furthermore, theoretical analysis and computational method of its cost threshold are provided to validate the effectiveness of the LCOR model. The results show that the LCOR model is effective for designing real-world networks with high robustness and less cost against cascading failure.     

复杂网络中带有应急恢复机理的级联动力学分析

提出带有应急恢复机理的网络级联故障模型,研究模型在最近邻耦合网络,Erdos-Renyi随机网络,Watts-Strogatz小世界网络和Barabasi-Albert无标度网络四种网络拓扑下的网络级联动力学行为.给出了应急恢复机理和网络效率的定义,并研究了模型中各参数对网络效率和网络节点故障率在级联故障过程中变化情况的影响.结果表明,模型中应急恢复概率的增大减缓了网络效率的降低速度和节点故障率的增长速度,并且提高了网络的恢复能力.而且网络中节点负载容量越大,网络效率降低速度和节点故障率的增长速度越慢.同时,随着节点过载故障概率的减小,网络效率的降低速度和节点故障率的增长速度也逐渐减缓.此外,对不同网络拓扑中网络效率和网络节点故障率在级联故障过程中的变化情况进行分析,结果发现网络拓扑节点度分布的异质化程度的增大,提高了级联故障所导致的网络效率的降低速度和网络节点故障率的增长速度.以上结果分析了复杂网络中带有应急恢复机理的网络级联动力学行为,为实际网络中级联故障现象的控制和防范提供了参考.     

A robust matching model of capacity to defense cascading failure on complex networks

How to control the cascading failure has become a hot topic in recent years. In this paper, we propose a new matching model of capacity by developing a profit function to defense cascading failures on artificially created scale-free networks and the real network structure of the North American power grid. Results show that our matching model can enhance the network robustness efficiently, which is particularly important for the design of networks to deduce the damage triggered by the cascading failures.     

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.     

基于层间相似性的时序网络节点重要性研究

时序网络可以更加准确地描述节点之间的交互顺序和交互关系.结合多层耦合网络分析法,本文提出了基于节点层间相似性的超邻接矩阵时序网络节点重要性识别方法,与经典的认为所有层间关系为常数不同,层间关系用节点的邻居拓扑重叠系数进行度量.Workspace和Enrons数据集上的结果显示:相比经典的方法,使用该方法得到的Kendall’sτ值在各时间层上的平均提高,最高为17.72%和12.44%,结果表明层间相似性的度量对于时序网络的节点重要性度量具有十分重要的意义.     

IKN-CF: An Approach to Identify Key Nodes in Inter-Domain Routing Systems Based on Cascading Failures

Inter-domain routing systems is an important complex network in the Internet. Research on the vulnerability of inter-domain routing network nodes is of great support to the stable operation of the Internet. For the problem of node vulnerability, we proposed a method for identifying key nodes in inter-domain routing systems based on cascading failures (IKN-CF). Firstly, we analyzed the topology of inter-domain routing network and proposed an optimal valid path discovery algorithm considering business relationships. Then, the reason and propagation mechanism of cascading failure in the inter-domain routing network were analyzed, and we proposed two cascading indicators, which can approximate the impact of node failure on the network. After that, we established a key node identification model based on improved entropy weight TOPSIS (EWT), and the key node sequence in the network can be obtained through EWT calculation. We compared the existing three methods in two real inter-domain routing networks. The results indicate that the ranking results of IKN-CF are high accuracy, strong stability, and wide applicability. The accuracy of the top 100 nodes of the ranking result can reach 83.6%, which is at least 12.8% higher than the average accuracy of the existing three methods.     

一种无线传感器网络健壮性可调的能量均衡拓扑控制算法

无线传感器网络中, 应用环境的干扰导致节点间距不能被准确度量. 所以利用以节点间距作为权重的闭包图(EG)模型构建的拓扑没有考虑环境的干扰, 忽略了这部分干扰带来的能耗, 缩短了网络生存时间. 针对无线传感器网络拓扑能量不均的特点和EG模型的缺陷, 首先引入节点度调节因子, 建立通信度量模型和节点实际生存时间模型; 其次量化网络节点度, 从而获取满足能量均衡和网络生命期最大化需求的节点度的取值规律; 然后利用该取值规律和函数极值充分条件解析推导出网络最大能量消耗值和最长生存时间, 并获得最优节点度; 最后基于以上模型提出一种健壮性可调的能量均衡拓扑控制算法. 理论证明该拓扑连通且为双向连通. 仿真结果说明网络能利用最优节点度达到较高的健壮性, 保证信息可靠传输, 且算法能有效平衡节点能耗, 提高网络健壮性, 延长网络生命周期.     

Load-redistribution strategy based on time-varying load against cascading failure of complex network

Cascading failure can cause great damage to complex networks, so it is of great significance to improve the network robustness against cascading failure. Many previous existing works on load-redistribution strategies require global information, which is not suitable for large scale networks, and some strategies based on local information assume that the load of a node is always its initial load before the network is attacked, and the load of the failure node is redistributed to its neighbors according to their initial load or initial residual capacity. This paper proposes a new load-redistribution strategy based on local information considering an ever-changing load. It redistributes the loads of the failure node to its nearest neighbors according to their current residual capacity, which makes full use of the residual capacity of the network. Experiments are conducted on two typical networks and two real networks, and the experimental results show that the new load-redistribution strategy can reduce the size of cascading failure efficiently.