Failures In Complex Networks Research Articles

Activity centrality-based critical node identification in complex systems against cascade failure

Identifying critical nodes in the network has been a concern permanently. Cascading failure would cause catastrophic events, and in the field of cascading failure in complex networks, the structure and dynamics are considered as the key in the process of cascading failure. It is vital to have an applicable centrality to find critical nodes that could control and prevent the cascading failure. In this paper, we propose a steady-state activity centrality to evaluate the importance of each node, and the proposed centrality is related to the degree of each node and the activity of its neighbor nodes. The giant component, the average activity, and the tipping point under different attack strategies are introduced to compare the attack effect of these three centralities including steady-state activity centrality, betweenness centrality and closeness centrality. The results show that the attack effect under the proposed centrality is better than the effect under the other two centralities. In particular, for the network with the SIS and gene regulation dynamic, the attack effect under the steady-state activity centrality driven strategy is obviously better than the effect under the betweenness centrality driven strategy when the network is heterogeneous.

Research on proactive defense and dynamic repair of complex networks considering cascading effects

Cascading effects can result in the nonlinear propagation of failures in complex networks, ultimately leading to network collapse. Research on the fault propagation principles, defense strategies, and repair strategies can help mitigate the effects of cascading failures. Especially, proactive defense and dynamic repair are flexible and effective methods to ensure network security. Most studies on the cascade of complex networks are based on the unprocessed initial information of the network. However, marginal nodes are a type of node that cloaks the initial information of the network. In this study, we rank the importance of nodes according to the intensity of network energy confusion after the removal of this node, clarify the meaning of marginal nodes and proposed two methods to screen marginal nodes. The results indicated that the proactive removal of marginal nodes can effectively reduce the effect of cascading failures without causing any negative disturbance to the energy flow of the network. In addition, network repair according to the proposed strategy can minimize the cascade effect in the repair process and improve repair efficiency.

A solution technique to cascading link failure prediction

The study of complex networks is a new powerful tool that can provide a profitable skeleton to better elucidate technology-related phenomena and interactions between components of real-world networks However, it is not easy to predict the communal behavior of such systems from their elements and on the other hand, the failure of one or few elements can trigger the failure of other elements throughout the network, resulting in network breakdown and catastrophic events at large scales. Therefore, developing predictive mathematical techniques to examine complex networks is one of the biggest challenges of the present time. Knowing that link failure prediction is less studied in the OR literature, the present study articulates a method to predict link failures in complex networks, which is primarily based on Bayesian Belief Networks (BBN) and TOPSIS. The method aims to predict failures based on the affective factors of failures in networks. To this end, effective factors of failures are first detected, and then the graph of the relationship of factors along with their weight is determined. After all, the method provides the prediction for future damaged components. The functionality of the method is validated by an extensive computational analysis employing simulation in scale-free, random, and actual international aviation networks and its performance is compared with other benchmark algorithms. The results and sensitivity analysis experiments arrive at prominent managerial insights and efficacious implications and show that our method can generate high-quality solutions in many networks.

Cascading failure analysis and critical node identification in complex networks

Cascading failures in complex networks have attracted widespread attention in recent years. In this paper, a cascade model is proposed to analyze the potential overloads of nodes and edges simultaneously. First, some theoretical results for regular networks are detailed by the cascade model. The results show that in ring networks, as long as the capacity of each node or edge exceeds twice its initial load, the networks still work normally when an arbitrary node or edge breaks down, and in regular networks the failure of the farthest edges is most likely to induce cascades and the robustness of regular networks becomes stronger with the increase in the number of edges. Furthermore, an indicator evaluating the damage of the cascades is introduced. The analysis on the robustness of some typical networks indicates that WS networks can resist cascading failures more effectively and the robustness performance of WS networks can be improved by increasing rewiring probabilities. In BA networks, the failure of a critical node may pull down the whole networks, while the networks still function normally even if any edge breaks down. Finally, a forecasting indicator, called modified betweenness centrality, is proposed to identify critical nodes and experimental results show that the proposed indicator outperforms other typical indicators in identifying critical nodes.

Robust analysis of cascading failures in complex networks

Many real-world complex systems, such as power grids, the Internet, transportation networks, and complex information systems networks, which can be modeled abstractly with complex networks, may exhibit coupling or interdependence when subjected to random failure or deliberate attacks, i.e., cascading failures. Therefore, we want to understand the robustness of complex networks against cascading failures. The cascading failure has a failure propagation process, and it is necessary to establish an appropriate propagation model as the research basis. Hence, we adopted a new and more universal cascading failure propagation model based on discrete dynamic system. Based on this propagation model and combined with risk assessment, we proposed several cascading robustness index for complex networks. Then we conducted numerical experiments on several types of existing complex networks and real-world network. These experiments confirm the feasibility and rationality of our proposed indicators to reflect the cascading robustness, which can provide a reference and value for simulation and protection of real-world interdependent networks.

Network isolators inhibit failure spreading in complex networks

In our daily lives, we rely on the proper functioning of supply networks, from power grids to water transmission systems. A single failure in these critical infrastructures can lead to a complete collapse through a cascading failure mechanism. Counteracting strategies are thus heavily sought after. In this article, we introduce a general framework to analyse the spreading of failures in complex networks and demostrate that not only decreasing but also increasing the connectivity of the network can be an effective method to contain damages. We rigorously prove the existence of certain subgraphs, called network isolators, that can completely inhibit any failure spreading, and we show how to create such isolators in synthetic and real-world networks. The addition of selected links can thus prevent large scale outages as demonstrated for power transmission grids.

Mitigation of cascading failures in complex networks

Cascading failures in many systems such as infrastructures or financial networks can lead to catastrophic system collapse. We develop here an intuitive, powerful and simple-to-implement approach for mitigation of cascading failures on complex networks based on local network structure. We offer an algorithm to select critical nodes, the protection of which ensures better survival of the network. We demonstrate the strength of our approach compared to various standard mitigation techniques. We show the efficacy of our method on various network structures and failure mechanisms, and finally demonstrate its merit on an example of a real network of financial holdings.

Erratum to: Cascading failures in complex networks

Erratum to: Cascading failures in complex networks

Cascading failures in complex networks

Abstract Cascading failure is a potentially devastating process that spreads on real-world complex networks and can impact the integrity of wide-ranging infrastructures, natural systems and societal cohesiveness. One of the essential features that create complex network vulnerability to failure propagation is the dependency among their components, exposing entire systems to significant risks from destabilizing hazards such as human attacks, natural disasters or internal breakdowns. Developing realistic models for cascading failures as well as strategies to halt and mitigate the failure propagation can point to new approaches to restoring and strengthening real-world networks. In this review, we summarize recent progress on models developed based on physics and complex network science to understand the mechanisms, dynamics and overall impact of cascading failures. We present models for cascading failures in single networks and interdependent networks and explain how different dynamic propagation mechanisms can lead to an abrupt collapse and a rich dynamic behaviour. Finally, we close the review with novel emerging strategies for containing cascades of failures and discuss open questions that remain to be addressed.

Cascades in coupled map lattices with heterogeneous distribution of perturbations

As an important aspect of network robustness, cascading failure in complex networks has attracted a tremendous amount of interest in recent years. In the paper, we propose a novel cascading failure model of coupled map lattices by introducing heterogeneous distribution of perturbations, where a number of nodes are perturbed at the initial attack. The performance of four general attacking strategies are explored, which shows that high-betweenness strategy outperforms three other attacking strategies when heterogeneous perturbation mechanism is adopted. The results also indicate that increasing the coupling strength on direct neighbors can make the network more vulnerable and accelerate the propagation speed of cascades. And a more compact network structure will restrain the range and the propagation speed of cascading failures. We verify the influence of the heterogeneous perturbation principle on two real-world networks. In general, the effect on two real networks is in good accordance with that of BA scale-free networks, which means that the model can serve as a powerful tool to study realistic network robustness against cascades. Our work gains insight into the robustness and vulnerability of complex networked systems with respect to cascading failures.

Cascading failures in complex networks caused by overload attacks

Complex networks are known to be vulnerable to the failure of components in terms of structural robustness. An as yet less researched topic is dynamical robustness, which refers to the ability of a network to maintain its dynamical activity against local disturbances. This paper introduces a new type of attack—the overload attack—to disturb the network’s dynamical activity. The attack is based on the load redistribution model for sequential attacks. The main contribution are heuristics to assess the vulnerability of complex networks with respect to this type of attack. The effectiveness of the heuristics is demonstrated with an application for real power networks.

Cascade phenomenon against subsequent failures in complex networks

Cascade phenomenon may lead to catastrophic disasters which extremely imperil the network safety or security in various complex systems such as communication networks, power grids, social networks and so on. In some flow-based networks, the load of failed nodes can be redistributed locally to their neighboring nodes to maximally preserve the traffic oscillations or large-scale cascading failures. However, in such local flow redistribution model, a small set of key nodes attacked subsequently can result in network collapse. Then it is a critical problem to effectively find the set of key nodes in the network. To our best knowledge, this work is the first to study this problem comprehensively. We first introduce the extra capacity for every node to put up with flow fluctuations from neighbors, and two extra capacity distributions including degree based distribution and average distribution are employed. Four heuristic key nodes discovering methods including High-Degree-First (HDF), Low-Degree-First (LDF), Random and Greedy Algorithms (GA) are presented. Extensive simulations are realized in both scale-free networks and random networks. The results show that the greedy algorithm can efficiently find the set of key nodes in both scale-free and random networks. Our work studies network robustness against cascading failures from a very novel perspective, and methods and results are very useful for network robustness evaluations and protections.

Controllability and observability of cascading failure networks

Cascading failure analysis in previous existing works has mainly focused on random or intentional local attacks, and how to control these failures in complex networks with minimum input from the external signals is a new way of understanding cascades from a global view of network control. In this paper, we are motivated to develop a new framework, which first transforms the original networks (ONs) into cascading failure networks (CFNs) via the attack on each single node. Then, we study the controllability of the CFNs, and try to disclose the cascading failures of the ONs by network control. Furthermore, we analyze the impact of network structure dynamics on the framework. The results show that large-scale cascades are more likely to be triggered by hub node attacks in sparse and inhomogeneous networks, which need more driver nodes in order for them to be controlled. The driver nodes in the CFNs tend to avoid the high-degree nodes in the ONs, and this tendency enhances the homogeneous networks. In addition, networks with strong community strength and heterogeneous community sizes are more robust against attacks, and are easier to control. We also find that the degree distribution of the ONs mainly determines the size of the CFNs, as well as the minimum number of driver nodes, and the latter is also applicable to their observability. Furthermore, a similar impact on the CFNs can be observed by increasing the number of links as well as the capacity of the nodes in the ONs.

Vulnerability of clustering under node failure in complex networks

Robustness in response to unexpected events is always desirable for real-world networks. To improve the robustness of any networked system, it is important to analyze vulnerability to external perturbation such as random failures or adversarial attacks occurring to elements of the network. In this paper, we study an emerging problem in assessing the robustness of complex networks: the vulnerability of the clustering of the network to the failure of network elements. Specifically, we identify vertices whose failures will critically damage the network by degrading its clustering, evaluated through the average clustering coefficient. This problem is important because any significant change made to the clustering, resulting from element-wise failures, could degrade network performance such as the ability for information to propagate in a social network. We formulate this vulnerability analysis as an optimization problem, prove its NP-completeness and non-monotonicity, and offer two algorithms to identify the vertices most important to clustering. Finally, we conduct comprehensive experiments in synthesized social networks generated by various well-known models as well as traces of real social networks. The empirical results over other competitive strategies show the efficacy of our proposed algorithms.

Mitigate Cascading Failures on Networks using a Memetic Algorithm.

Research concerning cascading failures in complex networks has become a hot topic. However, most of the existing studies have focused on modelling the cascading phenomenon on networks and analysing network robustness from a theoretical point of view, which considers only the damage incurred by the failure of one or several nodes. However, such a theoretical approach may not be useful in practical situation. Thus, we first design a much more practical measure to evaluate the robustness of networks against cascading failures, termed Rcf. Then, adopting Rcf as the objective function, we propose a new memetic algorithm (MA) named MA-Rcf to enhance network the robustness against cascading failures. Moreover, we design a new local search operator that considers the characteristics of cascading failures and operates by connecting nodes with a high probability of having similar loads. In experiments, both synthetic scale-free networks and real-world networks are used to test the efficiency and effectiveness of the MA-Rcf. We systematically investigate the effects of parameters on the performance of the MA-Rcf and validate the performance of the newly designed local search operator. The results show that the local search operator is effective, that MA-Rcf can enhance network robustness against cascading failures efficiently, and that it outperforms existing algorithms.

Failure-recovery model with competition between failures in complex networks: a dynamical approach

Real systems are usually composed by units or nodes whose activity can be interrupted and restored intermittently due to complex interactions not only with the environment, but also with the same system. Majdandžić et al (2014 Nat. Phys. 10 34) proposed a model to study systems in which active nodes fail and recover spontaneously in a complex network and found that in the steady state the density of active nodes can exhibit an abrupt transition and hysteresis depending on the values of the parameters. Here we investigate a model of recovery-failure from a dynamical point of view. Using an effective degree approach we find that the systems can exhibit a temporal sharp decrease in the fraction of active nodes. Moreover we show that, depending on the values of the parameters, the fraction of active nodes has an oscillatory regime which we explain as a competition between different failure processes. We also find that in the non-oscillatory regime, the critical fraction of active nodes presents a discontinuous drop which can be related to a ‘targeted’ k-core percolation process. Finally, using mean field equations we analyze the space of parameters at which hysteresis and oscillatory regimes can be found.

Effects of link-orientation methods on robustness against cascading failures in complex networks

Abstract Unidirectional and bidirectional links may coexist in many realistic networked complex systems such as the city transportation networks. Even more, for some considerations, several bidirectional links are shifted to unidirectional ones. Many link-orientation strategies might be employed, including High-to-Low, Low-to-High and Random direction-determining methods, abbreviated as HTLDD, LTHDD and RDD respectively. Traffic passing through a unidirectional link is restricted to one-side direction. In real complex systems, nodes are correlated with each other. The failure from an initial node may be propagated iteratively, resulting in a large scale of failures of other nodes, called cascade phenomenon which may damage the safety or security of the networked system. Assuming that traffic load on any failed node can be redistributed to its non-failed neighbors, in this work, we try to reveal the effects of unidirectional links on network robustness against cascades. Extensive simulations have been implemented on kinds of networks including Scale-Free networks, Small-World networks, and Erdos–Renyi random networks. The results showed that all of the above three direction-determining methods decrease the robustness of the original networks against cascading failure. This work can help network designers and managers understand the robustness of network well and efficiently prevent the safety events.

Load-redistribution strategy based on time-varying load against cascading failure of complex network**Project supported by the National Basic Research Program of China (Grant No. 2013CB328903), the Special Fund of 2011 Internet of Things Development of Ministry of Industry and Information Technology, China (Grant No. 2011BAJ03B13-2), the National Natural Science Foundation of China (Grant No. 61473050), and the Key Science and Technology

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.

Modeling of self-healing against cascading overload failures in complex networks

The development of online prognostic and fast-recovery technology promotes the realization of self-healing techniques. Considering the cascading overload failures as one of the major failure modes in real networks, we introduce a model for self-healing against overload propagation in complex networks due to malicious attack. Especially, we study the role of basic quantities (restoration timing and resource) in general self-healing restoration against cascading overload failures in network models of homogeneous (Erdős-Rényi) and heterogeneous (scale-free) networks. We demonstrate how networks during cascading failures can be saved from the brink of collapse by proper combination of both restoration timing and resource. And we find that optimal restoration timing for the model and realistic networks exists at a given restoration resource in the self-healing process.

Design Robust Networks against Overload-Based Cascading Failures

Cascading failures are an interesting phenomenon in the study of complex networks and have attracted great attention. Examples of cascading failures include disease epidemics, traffic congestion, and electrical power system blackouts. In these systems, if external shocks or excess loads at some nodes are propagated to other connected nodes because of failure, a domino effect often occurs with disastrous consequences. Therefore, how to prevent cascading failures in complex networks is emerging as an important issue. A vast amount of research has attempted to design large networked infrastructures with the capability to withstand failures and fluctuations; this can be thought of as an optimal design task. In this paper, a cascading failure on an overload-based model was studied and a novel core-periphery network topology was heuristically designed to mitigate the damage of cascading failures. Using the Largest Connected Component after a sequence of failures as the network robustness measure, numerical simulations show that the proposed network, which consists of a complete core of connected hub nodes and periphery nodes connecting to the core, is the least susceptible to cascading failures compared to other types of networks.