Efficient and robust routing on scale-free networks

Information routing is one of the most important problems in large communication networks. In this paper we propose a novel routing strategy in which the optimal paths between all pairs of nodes are chosen according to a cost function that incorporates degrees of nodes in paths. Results on large scale-free networks demonstrate that our routing strategy is more efficient than the shortest path algorithm and the efficient routing strategy proposed by Yan et al. [Phys. Rev. E 73, 046108 (2006)]. Furthermore our routing strategy has strong robustness against cascading failure attacks on networks.     

Comparison of cascading failures in small-world and scale-free networks subject to vertex and edge attacks

Complex networks may undergo a global cascade of overload failures when a single highly loaded vertex or edge is intentionally attacked. Here we use the recent load model of cascading failures to investigate the performance of the small-world (SW) and scale-free (SF) networks subject to deliberate attacks on vertex and edge. Simulation results suggest that compared with the SW network, the SF network is more vulnerable to deliberate vertex attacks and more robust to deliberate edge attacks. In the SF network, deliberate vertex attacks can result in larger cascading failures than deliberate edge attacks; however, in the SW network the situation is opposite. Furthermore, with the increase of the rewiring probability the SW network becomes more and more robust to deliberate vertex and edge attacks.     

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.     

Probability routing strategy for scale-free networks

This study proposes a probability routing strategy for improving traffic capability on scale-free networks. Compared with the shortest path routing strategy depending on central nodes largely and the efficient routing strategy avoiding hub routers as much as possible, the probability routing strategy makes use of hub routers more efficiently, transferring approximate average amount of packs of the whole network. Simulation results indicate that the probability routing strategy has the highest network capacity among the three routing strategies. This strategy provides network capacity that can be more than 30 times higher than that of the shortest path routing strategy and over 50% higher than that of the efficient routing strategy. In addition, the average routing path length of our proposed strategy is over 10% shorter than that of the efficient routing strategy and only about 10% longer than that of the shortest path routing strategy.     

Robustness analysis of network controllability

Structural controllability, which is an interesting property of complex networks, attracts many researchers from various fields. The maximum matching algorithm was recently applied to explore the minimum number of driver nodes, where control signals are injected, for controlling the whole network. Here we study the controllability of directed Erdös–Rényi and scale-free networks under attacks and cascading failures. Results show that degree-based attacks are more efficient than random attacks on network structural controllability. Cascade failures also do great harm to network controllability even if they are triggered by a local node failure.     

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.     

Model for cascading failures with adaptive defense in complex networks

<正>This paper investigates cascading failures in networks by considering interplay between the flow dynamic and the network topology,where the fluxes exchanged between a pair of nodes can be adaptively adjusted depending on the changes of the shortest path lengths between them.The simulations on both an artificially created scale-free network and the real network structure of the power grid reveal that the adaptive adjustment of the fluxes can drastically enhance the robustness of complex networks against cascading failures.Particularly,there exists an optimal region where the propagation of the cascade is significantly suppressed and the fluxes supported by the network are maximal. With this understanding,a costless strategy of defense for preventing cascade breakdown is proposed.It is shown to be more effective for suppressing the propagation of the cascade than the recent proposed strategy of defense based on the intentional removal of 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.     

How non-uniform tolerance parameter strategy changes the response of scale-free networks to failures

In this paper, we introduce a non-uniform tolerance parameter (TP) strategy (the tolerance parameter is characterized by the proportion between the unused capacity and the capacity of a vertex) and study how the non-uniform TP strategy influences the response of scale-free (SF) networks to cascading failures. Different from constant TP in previous work of Motter and Lai (ML), the TP in the proposed strategy scales as a power-law function of vertex degree with an exponent b. The simulations show that under low construction costs D, when b>0 the tolerance of SF networks can be greatly improved, especially at moderate values of b; When b<0 the tolerance gets worse, compared with the case of constant TP in the ML model. While for high D the tolerance declines slightly with the b, namely b<0 is helpful to the tolerance, and b>0 is harmful. Because for smaller b the cascade of the network is mainly induced by failures of most high-degree vertices; while for larger b, the cascade attributes to damage of most low-degree vertices. Furthermore, we find that the non-uniform TP strategy can cause changes of the structure and the load-degree correlation in the network after the cascade. These results might give insights for the design of both network capacity to improve network robustness under limitation of small cost, and for the design of strategies to defend cascading failures of networks.     

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.     

Incremental routing strategy on scale-free networks

The most important function of a network is for transporting traffic. Due to the low traffic capacity of network systems under the global shortest path routing, plenty of heuristic routing strategies are emerging. In this paper, we propose a heuristic routing strategy called the incremental routing algorithm to improve the traffic capacity of complex networks. We divide the routing process into N$N$(the network size) steps and, at each step, we heuristically calculate all the routes for one source node considering both the dynamic efficient betweenness centrality and node degree information. We do extensive simulations on scale-free networks to confirm the effectiveness of the proposed incremental routing strategy. The simulation results show that the traffic capacity has been enhanced by a substantial factor at the expense of a slight lengthening in the average path.     

Edge-based-attack induced cascading failures on scale-free networks

Most previous existing works on cascading failures only focused on attacks on nodes rather than on edges. In this paper, we discuss the response of scale-free networks subject to two different attacks on edges during cascading propagation, i.e., edge removal by either the descending or ascending order of the loads. Adopting a cascading model with a breakdown probability p of an overload edge and the initial load (k_ik_j)^α of an edge ij, where k_i and k_j are the degrees of the nodes connected by the edge ij and α is a tunable parameter, we investigate the effects of two attacks for the robustness of Barabási-Albert (BA) scale-free networks against cascading failures. In the case of α<1, our investigation by the numerical simulations leads to a counterintuitive finding that BA scale-free networks are more sensitive to attacks on the edges with the lowest loads than the ones with the highest loads, not relating to the breakdown probability. In addition, the same effect of two attacks in the case of α=1 may be useful in furthering studies on the control and defense of cascading failures in many real-life networks. We then confirm by the theoretical analysis these results observed in simulations.     

Effects of the cascading failures on scale-free traffic networks

In this paper, we consider the artificial scale-free traffic network with dynamic weights (cost) and focus on how the removal strategies (flow-based removal, betweenness-based removal and mix-based removal) affect the damage of cascading failures based on the user-equilibrium (UE) assignment, which ensures the balance of flow on the traffic network. Experiment simulation shows that different removal strategies can bring large dissimilarities of the efficiency and damage after the intentional removal of an edge. We show that the mix-based removal of a single edge might reduce the damage of cascading failures and delay the breakdown time, especially for larger reserve capacity coefficient α. This is particularly important for real-world networks with a highly hetereogeneous distribution of flow, i.e., traffic and transportation networks, logistics networks and electrical power grids.     

Efficient routing on small complex networks without buffers

In this paper, we are exploring strategies for the reduction of the congestion in the complex networks. The nodes without buffers are considered, so, if the congestion occurs, the information packets will be dropped. The focus is on the efficient routing. The routing strategies are compared using two generic models, i.e., Barabàsi–Albert scale-free network and scale-free network on lattice, and the academic router networks of the Netherlands and France. We propose a dynamic deflection routing algorithm which automatically extends path of the packet before it arrives at congested node. The simulation results indicate that the dynamic routing strategy can further reduce the number of dropped packets in a combination with the efficient path routing proposed by Yan et al. [5].     

Global forward-predicting dynamic routing for traffic concurrency space stereo multi-layer scale-free network

Many real communication networks, such as oceanic monitoring network and land environment observation network,can be described as space stereo multi-layer structure, and the traffic in these networks is concurrent. Understanding how traffic dynamics depend on these real communication networks and finding an effective routing strategy that can fit the circumstance of traffic concurrency and enhance the network performance are necessary. In this light, we propose a traffic model for space stereo multi-layer complex network and introduce two kinds of global forward-predicting dynamic routing strategies, global forward-predicting hybrid minimum queue(HMQ) routing strategy and global forward-predicting hybrid minimum degree and queue(HMDQ) routing strategy, for traffic concurrency space stereo multi-layer scale-free networks. By applying forward-predicting strategy, the proposed routing strategies achieve better performances in traffic concurrency space stereo multi-layer scale-free networks. Compared with the efficient routing strategy and global dynamic routing strategy, HMDQ and HMQ routing strategies can optimize the traffic distribution, alleviate the number of congested packets effectively and reach much higher network capacity.     

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.     

A packet routing strategy using neural networks on scale-free networks

We propose a dynamic packet routing strategy by using neural networks on scale-free networks. In this strategy, in order to determine the nodes to which the packets should be transmitted, we use path lengths to the destinations of the packets, and adjust the connection weights of the neural networks attached to the nodes from local information and the path lengths. The performances of this strategy on scale-free networks which have the same degree distribution and different degree correlations are compared to one another. Our numerical simulations confirm that this routing strategy is more effective than the shortest path based strategy on scale-free networks with any degree correlations and that the performance of our strategy on assortative scale-free networks is better than that on disassortative and uncorrelated scale-free networks.     

Robustness of spatial networks and networks of networks

Many complex networks have recently been recognized to involve significant interdependence between different systems. Motivation comes primarily from infrastructures like power grids and communications networks, but also includes areas such as the human brain and finance. Interdependence implies that when components in one system fail, they lead to failures in the same system or other systems. This can then lead to additional failures finally resulting in a long cascade that can cripple the entire system. Furthermore, many of these networks, in particular infrastructure networks, are embedded in space and thus have unique spatial properties that significantly decrease their resilience to failures. Here we present a review of novel results on interdependent spatial networks and how cascading processes are affected by spatial embedding. We include various aspects of spatial embedding such as cases where dependencies are spatially restricted and localized attacks on nodes contained in some spatial region of the network. In general, we find that spatial networks are more vulnerable when they are interdependent and that they are more likely to undergo abrupt failure transitions than interdependent non-embedded networks. We also present results on recovery in spatial networks, the nature of cascades due to overload failures in these networks, and some examples of percolation features found in real-world traffic networks. Finally, we conclude with an outlook on future possible research directions in this area.     

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.     

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.