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Mean–variance portfolios have been criticized because of unsatisfying out-of-sample performance and the presence of extreme and unstable asset weights. The bad performance is caused by estimation errors in inputs parameters, that is the covariance matrix and the expected return vector, especially the expected return vector. This topic has attracted wide attention. In this paper, we aim to find better portfolio optimization model to reduce the undesired impact of parameter uncertainty and estimation errors of mean–variance portfolio model. Firstly, we introduce a sparse mean–variance portfolio model, and give some insight about sparsity. Secondly, we propose two sparse and robust portfolio models by using objective function regularization and robust optimization. Finally, three empirical studies are proposed with real market data. • We introduce a sparse mean–variance portfolio model. • We propose two general sparse and robust portfolio models. • Three empirical studies with real market data are proposed. [ABSTRACT FROM AUTHOR]

We analyze the structural and functional robustness of networked critical infrastructure systems (CISs). We propose a structural and functional robustness model of a typical complex network and take into account the corresponding measuring metrics and cascading processes to assess the impact of different hazard modes on robustness. We analyze the robustness of the shanghai subway network and the central China power grid to demonstrate an application of the model. We find that both are strongly robust to random failure but extremely vulnerable to targeted attack. We identify the critical areas most likely to be attack targets and use a functional perspective to identify vulnerabilities. Our proposed method can be applied to other CISs and aid in understanding the mechanisms of network robustness. • The structural and functional robustness are analyzed. • The critical areas most likely to be attack targets are identified. • The fraction of the system after a series of failures occur are determined. • Overload failures are examined to determine how they propagate. [ABSTRACT FROM AUTHOR]

Abstract Cascading failures are emergent phenomena on interdependent networks and plenty of models have been proposed to explore the features of cascading failures. However, few of them focus on energy-supported dependence relations between interdependent networks including control nodes. In this paper, a load-based energy-supported cascading failure model is proposed on interdependent networks, where the energy control factor λ and control nodes are considered. According to the numerical simulations, it is found that as the energy control factor λ increases, both interdependent Erdős–Rényi (ER) networks and scale-free (SF) networks become more vulnerable. Meanwhile, with the increase of energy control factor λ , interdependent SF networks become more robust than ER networks against random failures. In addition, increasing the power exponent γ can improve the robustness of interdependent SF networks. Finally, although coupling preferences and control node setting strategies have few impacts on cascading failures on interdependent ER networks, the assortative coupling preference (AC) and betweenness control node setting strategy (BS) can improve the robustness of interdependent SF networks. Highlights • An energy-supported cascading failure model is proposed on interdependent networks. • Increasing factor λ makes interdependent SF networks more robust than ER networks. • Increasing exponent γ improves the robustness of interdependent SF networks. • The AC and BS can improve the robustness of interdependent SF networks. [ABSTRACT FROM AUTHOR]

Abstract In this paper the robust optimal control of deterministic information epidemics is inspected taking into consideration the noisy transition rates. Distinct from conventional works, the heterogeneous susceptible–infected–susceptible (SIS) model is adopted where both the heterogeneities in the network topology and the individual diversity are considered. In light of the commonly existing noise in the transition processes, we address the robust optimal control problem aiming at maximizing the spreading performance at the finite time instant given a fixed budget. By using the distribution analysis techniques, the inspected problem is transformed to a constrained optimal control problem and solved by the Pontryagin Maximum Principle (PMP). A novel approach combining the forward–backward sweep method and the secant method is proposed to efficiently reduce the computation burden. The performance of the robust optimal control as well as the influence of the parameters is examined by numerical experiments in real social networks. Highlights • Robust optimal control for information epidemics is addressed for the first time. • Heterogeneities in both network structure and transition processes are considered. • Computationally cheap algorithms is provided and tested in real networks. [ABSTRACT FROM AUTHOR]

Abstract Traffic incident detection is a very important research area of intelligent transportation systems. Many methods have obtained good performance in traffic incident detection. However, the robustness of these methods is not satisfactory. Namely, when one method is applied on another data set again, its performance is not always good, even it had obtained good performance on one data set once. In this paper, we propose an ensemble learning method to improve the robustness in traffic incident detection. The proposed method trains individual SVM and KNN models firstly. And then, it takes a strategy to combine them for better final output. Experimental results show that the propose method has achieved the best performance among all the compared methods. Also, the ensemble learning strategy in the proposed method has improved the robustness of the individual models. Highlights • This paper proposes a new ensemble learning method to detect traffic incidents. • The proposed method has achieved satisfactory accuracy in traffic incident detection. • More importantly, the proposed method has improved the robustness of traffic incident detection. [ABSTRACT FROM AUTHOR]

Abstract Is idiosyncratic volatility priced? The existing literature finds conflicting results on the cross-sectional relation between expected returns and idiosyncratic volatility. This paper examines the relation between idiosyncratic volatility and expected returns in Chinese Stock Market. We find there is a significantly positive relation between idiosyncratic volatility and expected returns when we use Fama–French five-factor model to estimate idiosyncratic volatility. However, the positive relation disappears when we use GARCH (1,1) model to estimate idiosyncratic volatility. This result indicates that in Chinese Stock Market, the idiosyncratic volatility premium is just an apparent phenomenon, whether the idiosyncratic volatility matter or not depend on the way we estimate the idiosyncratic volatility. The result is robust after controlling for investors' lottery preference, investors' sentiment and other factors. Highlights • A new method is applied to estimate idiosyncratic volatility. • The idiosyncratic volatility is positively related to expected return. • Positive relation disappears when using alternate estimate method. • In China, the idiosyncratic volatility premium is just an apparent phenomenon. [ABSTRACT FROM AUTHOR]

Abstract Cold-start link prediction has been a hot issue in complex network. Different with most of existing methods, this paper utilizes multiple interactions to predict a specific type of links. In this paper, multiple interactions are abstracted as multi-relational networks, and robust principle component analysis is employed to extract low-dimensional latent factors from sub-networks. Then a distribution free independence test, projection correlation, is introduced to efficiently analyze dependence between target and auxiliary sub-networks. Furthermore, associated auxiliary networks are exploited for cold-start link prediction, which aims to forecast potential links for new/isolated nodes in target sub-networks. Experimental results on 8 bioinformatics datasets validate rationality and effectiveness of the method. Highlights • An efficient method for network dependence analysis is proposed via projection correlation. • Two kind of methods with multiple interactions are proposed for cold-start link prediction. • It is promosing for cold start link prediction to establish regression between latent factors of sub-networks. [ABSTRACT FROM AUTHOR]

Abstract A concept of bypass rewiring on directed networks is proposed, and random bypass rewiring on infinite directed random networks is analytically and numerically investigated with double generating function formalisms and simulations. As a result, it is derived that random bypass rewiring makes infinite directed (undirected) random networks extremely robust for arbitrary occupation probabilities if and only if in-degree of every node except a fixed number of nodes is equal to the out-degree (every node except a finite number of nodes has even degree); random bypass rewiring can make the percolation threshold 0 on infinite directed (undirected) random networks. From the results on infinite random networks, it is generalized that a finite network has a strongly connected spanning subnetwork which has an Eulerian path or cycle if and only if there exists an way of bypass rewiring to make the finite network extremely robust for every combination of removed nodes; Eulerian networks are extremely robust with bypass rewiring for every combination of removed nodes. The generalized results say that bypass rewiring improves connectivity and robustness of not only infinite networks but also real-world networks, like the Internet, with a finite number of nodes. Highlights • A concept of bypass rewiring on directed networks is proposed. • Random bypass rewiring can guarantee extreme robustness of random networks. • Bypass rewiring can make the percolation threshold 0. • Bypass rewiring guarantees extreme robustness of Eulerian networks. • Bypass rewiring can guarantee extreme robustness of the Internet topology. [ABSTRACT FROM AUTHOR]

Abstract We present a systematic and detailed study of the robustness of directed networks under random and targeted removal of links. We work with a set of network models of random and scale free type, generated with specific features of clustering and assortativity. Various strategies like random deletion of links, or deletions based on betweenness centrality and degrees of source and target nodes, are used to breakdown the networks. The robustness of the networks to the sustained loss of links is studied in terms of the sizes of the connected components and the inverse path lengths. The effects of clustering and 2-node degree correlations, on the robustness to attack, are also explored. We provide specific illustrations of our study on three real-world networks constructed from protein–protein interactions and from transport data. Highlights • The study details the response and robustness of directed networks to loss of links. • It includes results on both standard network models as well as three real networks. • The strategies for removal of links are based on global and local network properties. • Responses are characterized by the extent and efficiency of structural connectivity. • The specific roles of clustering and 2-node degree correlations are also explored. [ABSTRACT FROM AUTHOR]

Abstract A bipartite network is a graph that contains two disjoint sets of nodes, such that every edge connects the two node sets. The significance of identifying influential nodes in bipartite networks is highlighted from both theoretical and practical perspectives. By considering the unique feature of bipartite networks, namely, links between the same node set are forbidden, we propose two new algorithms, called SVD-rank and SVDA-rank respectively. In the two algorithms, singular value decomposition (SVD) is performed on the original bipartite network and augmented network (two ground nodes are added). Susceptible–Infected–Recovered (SIR) model is employed to evaluate the performance of the two algorithms. Simulations on seven real-world networks show that the proposed algorithms can well identify influential spreaders in bipartite networks, and the two algorithms are robust to network perturbations. The proposed algorithms may have potential applications in the control of bipartite networks. Highlights • We proposed SVD-rank to identify influential spreaders in bipartite networks. • Inspired by the LeaderRank, we also proposed SVDA-rank. • Simulations on seven bipartite networks show effectiveness of the algorithms. • The proposed algorithms are robust to network perturbations. [ABSTRACT FROM AUTHOR]

Abstract Air transport is one of the key infrastructures of today's global economy. Connections between airports define airport networks, where nodes are cities served by airports, connected by edges if there is at least one direct flight connecting them. The aims of this research are to relate structural properties of airport networks which explain how these networks respond to isolation of critical nodes, and to gain insight into relevant socio-economic factors that influence the development of airport networks. We split the world airport network (WAN) into seven global region airport networks (GRANs), using the divisions established by OAG database. We gather information about structural properties of each GRAN determining core cities through k-core decomposition, and critical cities through robustness analysis. We find that differences of robustness across GRANs can be explained by the fraction of core cities relative to total cities. Furthermore, analysis of multilevel structure reveal relevant differences between GRANs, rooted on geographical and socio-economic factors, and give insight about how network robustness in airport networks can be enhanced. Highlights • This research relates structural determinants of regional airport networks robustness. • World airport network is divided into seven regions defined in OAG dataset. • We define core cities as the ones of the main core of k-core decomposition. • Critical cities are obtained through node selection criteria in robustness analysis. • Robustness of regional airport networks depends of the size of each main core. [ABSTRACT FROM AUTHOR]

Cascading failure is an ubiquitous phenomenon in many types of complex networks, and it has attracted significant concerns in the past decade. In this paper, we consider a generic transmission network consisting of two kinds of nodes, i.e., hosts and routers, and only the hosts can generate and receive packets. In such a host–router network model, the network robustness against cascading failure is closely related to the hosts’ locations. We employ the memetic algorithm (MA) to find a near-optimal way to locate the hosts, which remarkably improves the network robustness compared with three degree-based methods. Furthermore, we investigate the optimal configuration of the hosts given by the MA algorithm and put forward a faster method to select the hosts. This work provides a start point for systematically analyzing and optimizing network robustness of complex networks with heterogeneous node functions. [ABSTRACT FROM AUTHOR]

Cascading failures are widely found in hyper-networks. In this paper, a new cascading failure model based on couple map lattice is proposed in terms of the hyper-adjacent matrix and joint degree. The cascading failure model is rather universal describing the cascading failure behavior of k uniform hyper-network and many typical complex networks. Simulation results show that 3 uniform scale-free hyper-network is robust against random attacks but is vulnerable to deliberate attacks. In addition, a scale-free hyper-network is more robust than a general complex network against the same attack. Finally, an approximate solution to the disturbance threshold of k uniform scale-free hyper-network is obtained. [ABSTRACT FROM AUTHOR]

We consider an open-ended set of cultural features in the Axelrod model of cultural dissemination. By replacing the features in which a high degree of consensus is achieved by new ones, we address here an essential ingredient of societies: the evolution of topics as a result of social dynamics and debate. Our results show that, once cultural clusters have been formed, the introduction of new topics into the social debate has little effect on them, but it does have a significant influence on the cultural overlap. Along with the Monte Carlo simulations, we derive and numerically solve an equation for the stationary cultural overlap based on a mean-field approach which reproduces the qualitative behavior of the model. [ABSTRACT FROM AUTHOR]

Abstract Many real-world networks are exposed in complicated environments and may be destroyed easily by various kinds of attacks and errors. With no doubt it is of great significance to promote the anti-attack ability of systems. Besides, analyzing attack models is also of significance. The existing studies about network robustness conducted on weighted or unweighted networks have drawn the conclusion that scale-free networks are fragile under malicious attacks, where the precondition is that the cost of removing a node is equal. In fact, the cost of attacking different nodes is far from equal, thus, the removal cost should be taken into consideration when conducting attacks. In this paper, a malicious attack model considering the cost of attacking nodes, termed as Nodal Attack with Cost (NA C), is first proposed to depict the tolerance of networks. Furthermore, the limitation of resources drives us to design an optimization algorithm based on memetic algorithm (MA), termed as MA- NA C , to search for the optimal combination of nodes with the minimum cost which can destroy networks to the desired degree. The experimental results show that networks perform robust under the high degree adaptive (HDA) attack when there is a great difference between hub nodes and leaf nodes in the attack cost, yet the results are similar to previous studies on the condition that the attack cost gap is minor. In addition, MA- NA C is efficient in finding a relatively small attack cost. Based on the study of cost-optimized network structure and features of attacked nodes obtained by MA- NA C , we find that MA- NA C selects the target nodes by taking into account their effect on network structure, which contributes to the good optimization ability of MA- NA C. Highlights • Practical attacks make networks fragmented rather than make each node isolated. • An attack model considering the cost of attacking nodes is designed accordingly. • A memetic algorithm MA- NA C is proposed to find the relatively low attack cost. • The good performance of MA- NA C is validated on various networks. [ABSTRACT FROM AUTHOR]

Abstract The safety of metro networks has recently attracted great attention. In this study, we investigated how to allocate security resources in a metro network to enhance its robustness through a defense-attack approach. For each defense-attack model, the defense strategy was first applied to protect a certain proportion of influential nodes in the network and then an attack was executed on the protected network. The influential nodes were identified by eight strategies, one of which, the breadth-tree coefficient strategy, is proposed as a new approach. Simulations of five metro networks showed that attacks on nodes with the highest betweenness centrality value are the most effective for disrupting a metro network, while the robustness of the metro network can be enhanced more efficiently with the proposed breadth-tree coefficient strategy. We also found that the robustness of metro networks benefits less from scattered protected metro stations, since some neglected weakly connected nodes emerge among the optimal influencers. The study also provided insights into how topological features influence the robustness of metro networks. It demonstrated that loop lines and smaller transfer stations can provide more options for alternative routes and be less vulnerable to targeted attacks, which makes the metro network more robust in the face of accidents and terrorist attacks. Our study provides useful information for metro network managers to take decisive actions on how to allocate security resources to increase the robustness of their metro network and design a more robust metro system. Highlights • We investigate how to allocate security resources in a metro network to enhance its robustness through a defense-attack approach. • The proposed breadth-tree coefficient method is proved to be the most effective protective strategy for metro networks. • The robustness of metro networks benefits less from scattered protected metro stations. [ABSTRACT FROM AUTHOR]

Abstract The essential of existing methods for promoting network robustness is randomly exchanging the edges of networks. Without considering the network structure, the performance of these algorithms is limited. Therefore, we put forward a way for classifying the edges of networks into three types, which are valid edges, invalid edges and flexible edges. Then, a heuristic optimization algorithm, which is designed based on the edge classification (EC) against malicious attacks (MA), is proposed to improve the robustness of scale-free (RSF) network termed as EC-RS F MA. EC-RS F MA improves the robustness of scale-free networks by adjusting the number of edges of each type and changing the connection relation of the same type of edges under the constraint that the degree distribution remains to be unchanged. In the experiments, the performance of EC-RS F MA is validated on both synthetic and real-world networks. The results show that EC-RS F MA outperforms the existing algorithms. Highlights • A heuristic algorithm based on edge classification, termed as EC-RSF MA , is proposed. • EC-RSF MA can enhance the robustness of scale-free networks. • Two types of malicious attacks are studied. • EC-RSF MA outperforms the existing algorithms in experiments. [ABSTRACT FROM AUTHOR]

Assortativity is one of the important characteristics in real networks. To study the effects of this characteristic on the robustness of networks, we propose a percolation model on networks with assortative dependence group. The assortativity in this model means that the nodes with the same or similar degrees form dependence groups, for which one node fails, other nodes in the same group are very likely to fail. We find that the assortativity makes the nodes with large degrees easier to survive from the cascading failure. In this way, such networks are more robust than that with random dependence group, which also proves the assortative network is robust in another perspective. Furthermore, we also present exact solutions to the size of the giant component and the critical point, which are in agreement with the simulation results well. [ABSTRACT FROM AUTHOR]

Efficient robustness and fault tolerance of complex network is significantly influenced by its connectivity, commonly modeled by the structure of pairwise relations between network elements, i.e., nodes. Nevertheless, aggregations of nodes build higher-order structures embedded in complex network, which may be more vulnerable when the fraction of nodes is removed. The structure of higher-order aggregations of nodes can be naturally modeled by simplicial complexes, whereas the removal of nodes affects the values of topological invariants, like the number of higher-dimensional holes quantified with Betti numbers. Following the methodology of percolation theory, as the fraction of nodes is removed, new holes appear, which have the role of merger between already present holes. In the present article, relationship between the robustness and homological properties of complex network is studied, through relating the graph-theoretical signatures of robustness and the quantities derived from topological invariants. The simulation results of random failures and intentional attacks on networks suggest that the changes of graph-theoretical signatures of robustness are followed by differences in the distribution of number of holes per cluster under different attack strategies. In the broader sense, the results indicate the importance of topological invariants research for obtaining further insights in understanding dynamics taking place over complex networks. [ABSTRACT FROM AUTHOR]

Identifying missing interactions in complex networks, known as link prediction, is realized by estimating the likelihood of the existence of a link between two nodes according to the observed links and nodes’ attributes. Similar approaches have also been employed to identify and remove spurious links in networks which is crucial for improving the reliability of network data. In network science, the likelihood for two nodes having a connection strongly depends on their structural similarity. The key to address these two problems thus becomes how to objectively measure the similarity between nodes in networks. In the literature, numerous network similarity metrics have been proposed and their accuracy has been discussed independently in previous works. In this paper, we systematically compare the accuracy of 18 similarity metrics in both link prediction and spurious link elimination when the observed networks are very sparse or consist of inaccurate linking information. Interestingly, some methods have high prediction accuracy, they tend to perform low accuracy in identification spurious interaction. We further find that methods can be classified into several cluster according to their behaviors. This work is useful for guiding future use of these similarity metrics for different purposes. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Robustness plays a critical role in the controllability of complex networks to withstand failures and perturbations. Recent advances in the edge controllability show that the interaction strength among edges plays a more important role than network structure. Therefore, we focus on the effect of interaction strength on the robustness of edge controllability. Using three categories of all edges to quantify the robustness, we develop a universal framework to evaluate and analyze the robustness in complex networks with arbitrary structures and interaction strengths. Applying our framework to a large number of model and real-world networks, we find that the interaction strength is a dominant factor for the robustness in undirected networks. Meanwhile, the strongest robustness and the optimal edge controllability in undirected networks can be achieved simultaneously. Different from the case of undirected networks, the robustness in directed networks is determined jointly by the interaction strength and the network’s degree distribution. Moreover, a stronger robustness is usually associated with a larger number of driver nodes required to maintain full control in directed networks. This prompts us to provide an optimization method by adjusting the interaction strength to optimize the robustness of edge controllability. [ABSTRACT FROM AUTHOR]

The robustness of complex networks under attacks largely depends on the structure of a network and the nature of the attacks. Previous research on interdependent networks has focused on two types of initial attack: random attack and degree-based targeted attack. In this paper, a deliberate attack function is proposed, where six kinds of deliberate attacking strategies can be derived by adjusting the tunable parameters. Moreover, the robustness of four types of interdependent networks (BA–BA, ER–ER, BA–ER and ER–BA) with different coupling modes (random, positive and negative correlation) is evaluated under different attacking strategies. Interesting conclusions could be obtained. It can be found that the positive coupling mode can make the vulnerability of the interdependent network to be absolutely dependent on the most vulnerable sub-network under deliberate attacks, whereas random and negative coupling modes make the vulnerability of interdependent network to be mainly dependent on the being attacked sub-network. The robustness of interdependent network will be enhanced with the degree–degree correlation coefficient varying from positive to negative. Therefore, The negative coupling mode is relatively more optimal than others, which can substantially improve the robustness of the ER–ER network and ER–BA network. In terms of the attacking strategies on interdependent networks, the degree information of node is more valuable than the betweenness. In addition, we found a more efficient attacking strategy for each coupled interdependent network and proposed the corresponding protection strategy for suppressing cascading failure. Our results can be very useful for safety design and protection of interdependent networks. [ABSTRACT FROM AUTHOR]

Most existing cascading failure mitigation strategy of power grids based on complex network ignores the impact of electrical characteristics on dynamic performance. In this paper, the robustness of the power grid under a power decentralization strategy is analysed through cascading failure simulation based on AC flow theory. The flow-sensitive (FS) centrality is introduced by integrating topological features and electrical properties to help determine the siting of the generation nodes. The simulation results of the IEEE-bus systems show that the flow-sensitive centrality method is a more stable and accurate approach and can enhance the robustness of the network remarkably. Through the study of the optimal flow-sensitive centrality selection for different networks, we find that the robustness of the network with obvious small-world effect depends more on contribution of the generation nodes detected by community structure, otherwise, contribution of the generation nodes with important influence on power flow is more critical. In addition, community structure plays a significant role in balancing the power flow distribution and further slowing the propagation of failures. These results are useful in power grid planning and cascading failure prevention. [ABSTRACT FROM AUTHOR]

Random decision making in genetic switches can be modeled as tossing a biased coin. In other word, each genetic switch can be considered as a game in which the reactive elements compete with each other to increase their molecular concentrations. The existence of a very small number of reactive element molecules has caused the neglect of effects of noise to be inevitable. Noise can lead to undesirable cell fate in cellular differentiation processes. In this paper, we study the robustness to noise in genetic switches by considering another switch to have a new gene regulatory network (GRN) in which both switches have been affected by the same noise and for this purpose, we will use Parrondo’s paradox. We introduce two networks of games based on possible regulatory relations between genes. Our results show that the robustness to noise can increase by combining these noisy switches. We also describe how one of the switches in network II can model lysis/lysogeny decision making of bacteriophage lambda in Escherichia coli and we change its fate by another switch. [ABSTRACT FROM AUTHOR]

In this paper, the performance of metro networks is studied from a network science perspective. We review the structural efficiency of metro networks on the basis of a passenger’s intuitive routing strategy that optimizes the number of transfers and the distance traveled.A new node centrality measure, called node occupying probability , is introduced for evaluating the level of utilization of stations. The robustness of a metro network is analyzed under several attack scenarios. Six metro networks (Beijing, London, Paris, Hong Kong, Tokyo and New York) are compared in terms of the node occupying probability and a few other performance parameters. Simulation results show that the New York metro system has better topological efficiency, the Tokyo and Hong Kong systems are the most robust under random attack and target attack , respectively. [ABSTRACT FROM AUTHOR]

Many crucial real-world networks could be modeled as scale-free networks, which play an important role in the human society. Once these functional network systems suffer from cascading failures, they may lead to the malfunction of the rest part of networks. In recent years, the researches on cascading failures of scale-free networks have drawn great attention, and many studies focused on modeling the cascading phenomena and studying how to improve the robustness of networks against failures. However, the scale-free networks used in most existing studies are with fixed network parameters including scaling exponent and assortativity, which is segmentary for depicting the functionality of networked systems comprehensively. Therefore, in this paper, a series of generated scale-free networks with a certain range of parameters is adopted to evaluate the robustness against cascading failures. In addition, to make an accurate description of the ability of scale-free networks against cascading failures, we propose a link-based robustness index. The results show that influenced by the network structure, the enlargement of assortativity makes the networks weaker to resist node-based cascading failures, yet the impact on promoting link-based robustness is not clear enough. With higher scaling exponents, the tolerance of scale-free networks against link-based cascading failures decreases, however, it does not show obvious relation to node-based robustness. [ABSTRACT FROM AUTHOR]

Cascading failures in communication networks with heterogeneous node functions are studied in this paper. In such networks, the traffic dynamics are highly dependent on the traffic generation patterns which are in turn determined by the locations of the hosts. The data-packet traffic model is applied to Barabási–Albert scale-free networks to study the cascading failures in such networks and to explore the effects of traffic generation patterns on network robustness. It is found that placing the hosts at high-degree nodes in a network can make the network more robust against both intentional attacks and random failures. It is also shown that the traffic generation pattern plays an important role in network design. [ABSTRACT FROM AUTHOR]

The robustness research of networked systems has drawn widespread attention in the past decade, and one of the central topics is to protect the network from external attacks through allocating appropriate defense resource to different nodes. In this paper, we apply a specific particle swarm optimization (PSO) algorithm to optimize the defense resource allocation in scale-free networks. Results reveal that PSO based resource allocation shows a higher robustness than other resource allocation strategies such as uniform, degree-proportional, and betweenness-proportional allocation strategies. Furthermore, we find that assigning less resource to middle-degree nodes under small-scale attack while more resource to low-degree nodes under large-scale attack is conductive to improving the network robustness. Our work provides an insight into the optimal defense resource allocation pattern in scale-free networks and is helpful for designing a more robust network. [ABSTRACT FROM AUTHOR]

Complex network response to node loss is a central question in different fields of network science because node failure can cause the fragmentation of the network, thus compromising the system functioning. Previous studies considered binary networks where the intensity (weight) of the links is not accounted for, i.e. a link is either present or absent. However, in real-world networks the weights of connections, and thus their importance for network functioning, can be widely different. Here, we analyzed the response of real-world and model networks to node loss accounting for link intensity and the weighted structure of the network. We used both classic binary node properties and network functioning measure, introduced a weighted rank for node importance (node strength), and used a measure for network functioning that accounts for the weight of the links (weighted efficiency). We find that: (i) the efficiency of the attack strategies changed using binary or weighted network functioning measures, both for real-world or model networks; (ii) in some cases, removing nodes according to weighted rank produced the highest damage when functioning was measured by the weighted efficiency; (iii) adopting weighted measure for the network damage changed the efficacy of the attack strategy with respect the binary analyses. Our results show that if the weighted structure of complex networks is not taken into account, this may produce misleading models to forecast the system response to node failure, i.e. consider binary links may not unveil the real damage induced in the system. Last, once weighted measures are introduced, in order to discover the best attack strategy, it is important to analyze the network response to node loss using nodes rank accounting the intensity of the links to the node. [ABSTRACT FROM AUTHOR]

Robustness of complex networks has been extensively studied via the notion of site percolation, which typically models independent and non-adaptive attacks (or disruptions). However, real-life attacks are often dependent and/or adaptive . This motivates us to characterize the robustness of complex networks, including non-interdependent and interdependent ones, against dependent and adaptive attacks. For this purpose, dependent attacks are accommodated by L -hop percolation where the nodes within some L -hop ( L ≥ 0 ) distance of a chosen node are all deleted during one attack (with L = 0 degenerating to site percolation). Whereas, adaptive attacks are launched by attackers who can make node-selection decisions based on the network state in the beginning of each attack. The resulting characterization enriches the body of knowledge with new insights, such as: (i) the Achilles’ Heel phenomenon is only valid for independent attacks, but not for dependent attacks; (ii) powerful attack strategies (e.g., targeted attacks and dependent attacks, dependent attacks and adaptive attacks) are not compatible and cannot help the attacker when used collectively. Our results shed some light on the design of robust complex networks. [ABSTRACT FROM AUTHOR]

Reputation is a valuable asset in online social lives and it has drawn increased attention. Due to the existence of noisy ratings and spamming attacks, how to evaluate user reputation in online rating systems is especially significant. However, most of the previous ranking-based methods either follow a debatable assumption or have unsatisfied robustness. In this paper, we propose an iterative group-based ranking method by introducing an iterative reputation–allocation process into the original group-based ranking method. More specifically, the reputation of users is calculated based on the weighted sizes of the user rating groups after grouping all users by their rating similarities, and the high reputation users’ ratings have larger weights in dominating the corresponding user rating groups. The reputation of users and the user rating group sizes are iteratively updated until they become stable. Results on two real data sets with artificial spammers suggest that the proposed method has better performance than the state-of-the-art methods and its robustness is considerably improved comparing with the original group-based ranking method. Our work highlights the positive role of considering users’ grouping behaviors towards a better online user reputation evaluation. [ABSTRACT FROM AUTHOR]

Here, we present a study on how the structure of semantic networks based on cliques (specifically, article titles) behaves when vertex removal strategies (i.e., random and uniform vertex removal — RUR, highest degree vertex removal — HDR, and highest intermediation centrality vertex removal — HICR) are applied to this type of network. We propose a method for calculation of the average size of the small components and we identify the existence of a fraction ( f p ) where the topological structure of the network changes. Semantic networks based on cliques maintain the small-world phenomenon when subjected to RUR, HDR and HICR for fractions of removed vertices less than or equal to f p . [ABSTRACT FROM AUTHOR]

It is demonstrated that controlling complex networks in practice needs more inputs than that predicted by the structural controllability framework. Besides, considering the networks usually faces to the external or internal failure, we define parameters to evaluate the control cost and the variation of controllability after cascades, exploring the effect of number of control inputs on the controllability for random networks and scale-free networks in the process of cascading failure. For different topological networks, the results show that the robustness of controllability will be stronger through allocating different control inputs and edge capacity. [ABSTRACT FROM AUTHOR]

A key ingredient of studying the topological evolution of covert network is the individual behaviors which generate the evolutionary dynamics of covert organizational network. In this paper, we proposed an improved preference measurement method and used it to analyze three evolutionary behaviors of a real covert network, namely node addition, node deletion and link formation. Simulation experiment demonstrated that the improved method is robust on the small organizational network. The empirical study showed the specific pattern of evolutionary behaviors by offering direct quantitative support from preferential measurement. The measured property is then extended from degree to multiple node properties. The results indicate that the preferences of different behaviors follow different distributions with linear or nonlinear tendency across the process according to the type of node property. We conclude that the general scale-free network model is not suitable to model the evolutionary process of covert network. [ABSTRACT FROM AUTHOR]

A question in the robustness research of networks, which has not been addressed previously but may be more important and of wider interest, is how to consider spatio-temporal tolerance against failure propagation after a fraction f of nodes attacked. Here we develop a quantitative approach to examine the cascading overload condition based on the structure connectivity when a fraction f of nodes is attacked randomly. We also explore the critical threshold against cascading failures with two types of load redistribution rule. Fixing the value of β (the redistribution parameter) or τ (the initial load distribution parameter), we prove that the network shows the strongest robustness when the values of β is equal to τ , and the network robustness shows a growth trend with the decrease of f . We get a striking conclusion within the global load preferential sharing rule that the network robustness is independent of the network topology. [ABSTRACT FROM AUTHOR]

The robustness of scale-free networks has attracted increasing attentions recently. It has been shown that scale-free networks are tolerant to random failures but fragile under malicious attacks. However, most existing studies focus on scale-free networks with fixed exponent (around 3) and assortativity (around 0), and the relationship between robustness and these parameters has not been studied systematically. Therefore, in this paper, we study the change of robustness along with different parameters, including scaling exponent and assortativity, of scale-free networks; moreover, the robustness of interdependent networks is also studied. In the experiments, synthetic single scale-free networks with varying scaling exponents are constructed and adjusted to fix assortativity. Several measures are adopted to estimate the robustness of networks under malicious and random attacks. Then, interdependent networks with varying parameters are constructed and their robustness against malicious attacks is studied. The results show that there is a positive correlation between robustness against node attacks and the scaling exponent as well as assortativity, and the positive correlation also exists in interdependent networks. [ABSTRACT FROM AUTHOR]

An assembly supply chain network (ASCN) is composed of manufacturers located in different geographical regions. To analyze the robustness of this ASCN when it suffers from catastrophe disruption events, we construct a cascading failure model of risk propagation. In our model, different disruption scenarios s are considered and the probability equation of all disruption scenarios is developed. Using production capability loss as the robustness index (RI) of an ASCN, we conduct a numerical simulation to assess its robustness. Through simulation, we compare the network robustness at different values of linking intensity and node threshold and find that weak linking intensity or high node threshold increases the robustness of the ASCN. We also compare network robustness levels under different disruption scenarios. [ABSTRACT FROM AUTHOR]

Cascading failure is fatal in applications and its investigation is essential and therefore became a focal topic in the field of complex networks in the last decade. In this paper, a cascading failure model is established for interconnected networks and the associated data-packet transport problem is discussed. A distinguished feature of the new model is its utilization of fuzzy information in resisting uncertain failures and malicious attacks. We numerically find that the giant component of the network after failures increases with tolerance parameter for any coupling preference and attacking ambiguity. Moreover, considering the effect of the coupling probability on the robustness of the networks, we find that the robustness of the assortative coupling and random coupling of the network model increases with the coupling probability. However, for disassortative coupling, there exists a critical phenomenon for coupling probability. In addition, a critical value that attacking information accuracy affects the network robustness is observed. Finally, as a practical example, the interconnected AS-level Internet in South Korea and Japan is analyzed. The actual data validates the theoretical model and analytic results. This paper thus provides some guidelines for preventing cascading failures in the design of architecture and optimization of real-world interconnected networks. [ABSTRACT FROM AUTHOR]

The robustness of complex network is a core issue in complex network research. We agree that not all overload nodes will be removed from the network in real networks because some effective measures can be taken to protect them. But only a few researches consider this issue. Based on previous researches, we propose a cascading model with an improved breakdown probability. Different from previous breakdown probability model, the current model brings in some parameters to explore the optimal distribution strategy of the protection resources. Furthermore, we quantify the allocation of the protection resources. We explore the relationship between the parameters of our cascading model and the robustness of three networks (two typical networks and one real network), based on which we find out the optimal value of the parameter. It in turn helps us to quantify the allocation of protection resources and form an optimal protection strategy. Our work may be helpful for improving the robustness of complex networks. [ABSTRACT FROM AUTHOR]

Many previous studies on link prediction have focused on using common neighbors to predict the existence of links between pairs of nodes. More broadly, research into the structural properties of evolving temporal networks and temporal link prediction methods have recently attracted increasing attention. In this study, for the first time, we examine the use of links between a pair of nodes to predict their common neighbors and analyze the relationship between the weight and the structure in static networks, evolving networks, and in the corresponding randomized networks. We propose both new unweighted and weighted prediction methods and use six kinds of real networks to test our algorithms. In unweighted networks, we find that if a pair of nodes connect to each other in the current network, they will have a higher probability to connect common nodes both in the current and the future networks—and the probability will decrease with the increase of the number of neighbors. Furthermore, we find that the original networks have their particular structure and statistical characteristics which benefit link prediction. In weighted networks, the prediction algorithm performance of networks which are dominated by human factors decrease with the decrease of weight and are in general better in static networks. Furthermore, we find that geographical position and link weight both have significant influence on the transport network. Moreover, the evolving financial network has the lowest predictability. In addition, we find that the structure of non-social networks has more robustness than social networks. The structure of engineering networks has both best predictability and also robustness. [ABSTRACT FROM AUTHOR]

The problem of finding the best strategy to attack a network or immunize a population with a minimal number of nodes has attracted much current research interest. The assessment of node importance has been a fundamental issue in the research of complex networks. In this paper, we propose a new concept called mapping entropy (ME) to identify the importance of a node in the complex network. The concept is established according to the local information which considers the correlation among all neighbors of a node. We evaluate the efficiency of the centrality by static and dynamic attacks on standard network models and real-world networks. The simulation result shows that the new centrality is more efficient than traditional attack strategies, whether it is static or dynamic. [ABSTRACT FROM AUTHOR]

Evaluating the importance of nodes for complex networks is of great significance to the research of survivability and robusticity of networks. This paper proposes an effective ranking method based on degree value and the importance of lines. It can well identify the importance of bridge nodes with lower computational complexity. Firstly, the properties of nodes that are connected to a line are used to compute the importance of the line. Then, the contribution of nodes to the importance of lines is calculated. Finally, degree of nodes and the contribution of nodes to the importance of lines are considered to rank the importance of nodes. Five real networks are used as test data. The experimental results show that our method can effectively evaluate the importance of nodes for complex networks. [ABSTRACT FROM AUTHOR]

Many networks in reality face a dynamic iteration of attacking and defending, in which attackers and defenders take turns to destroy and replenish networks. The framework of iterative attacking and defending has been introduced, and Kim and Anderson gave an iterative model with much finer granularity and empirically studied three attack/defense strategies on nodes. However, in real-world networks, the failure can also occur on links. We therefore extend the iterative attack/defense strategies to links and apply the robustness measure R and the link-robustness R l to evaluate the performance of each attack/defense strategy. Through intensive experiments on several well-known networks, the defense strategy of connecting nodes with low-centrality is effective enough to maintain network connectivity and increase the network robustness R against targeted node attacks, but it cannot enhance the link-robustness R l against malicious link attacks during the iterative rounds. Significantly, on two real-world networks, this strategy is perfect for simultaneously enhancing the robustness R and the link-robustness R l . [ABSTRACT FROM AUTHOR]

Failures of real-world infrastructure networks due to natural disasters often originate in a certain region, but this feature has seldom been considered in theoretical models. In this article, we introduce a possible failure pattern of geographical networks–“regional failure”–by which nodes and edges within a region malfunction. Based on a previous spatial network model (Louf et al., 2013), we study the robustness of geographical networks against regional failure, which is measured by the fraction of nodes that remain in the largest connected component, via simulations. A small-area failure results in a large reduction of their robustness measure. Furthermore, we investigate two pre-deployed mechanisms to enhance their robustness: One is to extend the cost–benefit growth mechanism of the original network model by adding more than one link in a growth step, and the other is to strengthen the interconnection of hubs in generated networks. We measure the robustness-enhancing effects of both mechanisms on the basis of their costs, i.e., the amount of excessive links and the induced geographical length. The latter mechanism is better than the former one if a normal level of costs is considered. When costs exceed a certain level, the former has an advantage. Because the costs of excessive links affect the investment decision of real-world infrastructure networks, it is practical to enhance their robustness by adding more links between hubs. These results might help design robust geographical networks economically. [ABSTRACT FROM AUTHOR]

Coupled systems used to increase capacity were shown beneficial as long as it does not open pathways to cascades. Previous studies on the robustness of coupled networks except for interdependent networks are almost the cases of random attack. Many challenges remain exist in targeted-attack problem of coupled networks. Since nodes within coupled networks show different functions for each network, this paper both analytically and numerically analyzed the robustness of coupled networks under three types of targeted attacking strategies, including attacking on nodes by considering internal and external degree, internal degree only, and external degree only. For coupled network with both interdependent and interconnected links, all degree distributions of intra- and inter-connectivity links are Poissonian, we find the system undergoes from second to first order phase transition as coupling strength q increases. The fraction of nodes in the giant component P ∞ at stable state, the critical phase transition threshold p c (first order threshold p c I and second order threshold p c I I ), and the critical point ( p c , q c ) separating the first and second order phase transitions are analytically obtained for three types of attacking strategies with attacking probability parameter α = 0 , 1 . We also find the system becomes more vulnerable as the average degree of intra-links k ̄ or inter-links K ̄ decreases. Therefore, the minimum average degrees k ̄ m i n and K ̄ m i n to maintain the system stable are obtained for the case of α = 0 , 1 . Moreover, we discussed three typical cases of coupled networks, interdependent networks ( K ̄ = 0 ), interacting networks ( q = 0 ) and bipartite network ( k = 0 , q = 0 ), the analytical expressions of P ∞ , p c and ( p c , q c ) (only for interdependent) are given respectively. Besides, we study the equivalence relations between interdependent networks and coupled networks with connectivity and dependency links for the same p c . The results imply that we can adjust the parameters q , k ̄ and K ̄ to make the two systems have the same robustness. Moreover, the results imply that one should not only protect nodes with high degree of intra-links or inter-links, but also defend nodes, the sum of whose degree of intra-links and inter-links is big, can avoid the system becoming vulnerable. [ABSTRACT FROM AUTHOR]

In this paper, we employ a nonparametric framework to robustly estimate the functional forms of drift and diffusion terms from discrete stationary time series. The proposed method significantly improves the accuracy of the parameter estimation. In this framework, drift and diffusion coefficients are modeled through orthogonal Legendre polynomials. We employ the least squares regression approach along with the Euler–Maruyama approximation method to learn coefficients of stochastic model. Next, a numerical discrete construction of mean squared prediction error (MSPE) is established to calculate the order of Legendre polynomials in drift and diffusion terms. We show numerically that the new method is robust against the variation in sample size and sampling rate. The performance of our method in comparison with the kernel-based regression (KBR) method is demonstrated through simulation and real data. In case of real dataset, we test our method for discriminating healthy electroencephalogram (EEG) signals from epilepsy ones. We also demonstrate the efficiency of the method through prediction in the financial data. In both simulation and real data, our algorithm outperforms the KBR method. [ABSTRACT FROM AUTHOR]

Recently, the study of optimizing network robustness has attracted increasing attentions, and the constraint that every node’s degree cannot be changed is considered. Although this constraint maintains the node degree distribution consistently in order to reserve the structure of networks, it makes the network structure be lack of flexibility since many network structure always transform in the modern society. Given this consideration, in this paper, we analyze the robustness of networks through setting a new constraint; that is, only the number of edges should be unchanged. Then, we use the link-robustness index ( R l ) as the measure of the network robustness against either random failures or intentional attacks, and make a comparative analysis of network robustness against different types of link attacks. Moreover, we use four types of networks as initial networks, namely scale-free networks, random networks, regular networks, and small-world networks. The experimental results show that the values of robustness measures for the optimized networks starting from different initial networks are similar under different link attacks, but the network topologies may be different. That is to say, networks with different topologies may have similar robustness in terms of the robustness measures. We also find that the optimized networks obtained by one link attack may not robust against other link attacks, sometimes, even weaker than the original networks. Therefore, before building networks, it is better to study which type of link attacks may happen. [ABSTRACT FROM AUTHOR]

Cascading failures in interconnected networks have received more and more attention. In previous works, the basic assumption is that networks share the same capacity redundancy. However, this setting cannot capture the real case very well. Hence, in this paper, we analyze the effect of capacity redundancy disparity on the robustness of interconnected networks. In isolated networks, it is well known that the complex network’s robustness can be improved by increasing its capacity redundancy. In interconnected networks where two networks share the same capacity redundancy, the similar result holds. Yet this result is not necessarily true in interconnected networks where two networks are different in capacity redundancy. We find that when the capacity redundancy of one network is fixed, the robustness of the whole system may not follow another network’s capacity redundancy. More specifically, when the fixed network’s capacity redundancy is very small or very large, the robustness of the whole system increases as another network’s capacity redundancy increases. But there exists a certain range within which the increase of one network’s capacity redundancy results in the robustness decline of the whole system. This counterintuitive feature appears under different coupling patterns such as assortative, disassortative, or random coupling. This result advances our understanding of the robustness of interconnected networks. [ABSTRACT FROM AUTHOR]

We focus on the optimization of network robustness with respect to intentional attacks on high-degree nodes. Given an existing network, this problem can be considered as a typical single-objective combinatorial optimization problem. Based on the heuristic Tabu Search optimization algorithm, a link-rewiring method is applied to reconstruct the network while keeping the degree of every node unchanged. Through numerical simulations, BA scale-free network and two real-world networks are investigated to verify the effectiveness of the proposed optimization method. Meanwhile, we analyze how the optimization affects other topological properties of the networks, including natural connectivity, clustering coefficient and degree–degree correlation. The current results can help to improve the robustness of existing complex real-world systems, as well as to provide some insights into the design of robust networks. [ABSTRACT FROM AUTHOR]