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.     

Robustness of heterogeneous complex networks

In this paper we study the robustness of heterogeneous preferential attachment networks. The robustness of a network measures its structural tolerance to the random removal of nodes and links. We numerically analyze the influence of the affinity parameters on a set of ensemble-averaged robustness metrics. We show that the presence of heterogeneity does not fundamentally alter the smooth nature of the fragmentation process of the models. We also show that a moderate level of locality translates into slight improvements in the robustness metrics, which prompts us to conjecture an evolutionary argument for the existence of real networks with power-law scaling in their connectivity and clustering distributions.     

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.     

Robustness of networks against cascading failures

Inspired by other related works, this paper proposes a non-linear load-capacity model against cascading failures, which is more suitable for real networks. The simulation was executed on the B-A scale-free network, E-R random network, Internet AS level network, and the power grid of the western United States. The results show that the model is feasible and effective. By studying the relationship between network cost and robustness, we find that the model can defend against cascading failures better and requires a lower investment cost when higher robustness is required.     

Robustness analysis of static routing on networks

Robustness is one of the crucial properties that needs to be considered in the design of routing strategies on networks. We study the robustness of three typical routing strategies, which are the SP (shortest path), EP (efficient path), and OP (optimal path) strategies, by simulating several different kinds of attacks including random attacks, target attacks and cascading failures on scale-free networks. Results of the average path length, betweenness centrality, network capacity, etc., demonstrate that the EP strategy is more robust than the other two, and the OP strategy is more reliable than the SP strategy in general. However, on the power-grid network, the OP strategy is more resistant against cascading failures than the EP and SP strategies.     

Robustness of optimal synchronization in real networks

Experimental studies can provide powerful insights into the physics of complex networks. Here, we report experimental results on the influence of connection topology on synchronization in fiber-optic networks of chaotic optoelectronic oscillators. We find that the recently predicted nonmonotonic, cusplike synchronization landscape manifests itself in the rate of convergence to the synchronous state. We also observe that networks with the same number of nodes, same number of links, and identical eigenvalues of the coupling matrix can exhibit fundamentally different approaches to synchronization. This previously unnoticed difference is determined by the degeneracy of associated eigenvectors in the presence of noise and mismatches encountered in real-world conditions.     

Robustness measurement of scale-free networks based on motif entropy

As a classical complex network model, scale-free network is widely used and studied. And motifs, as a high-order subgraph structure, frequently appear in scale-free networks, and have a great influence on the structural integrity, functional integrity and dynamics of the networks. In order to overcome the shortcomings in the existing work on the robustness of complex networks, only nodes or edges are considered, while the defects of high-order structure in the network are ignored. From the perspective of network motif, we propose an entropy of node degree distribution based on motif to measure the robustness of scale-free networks under random attacks. The effectiveness and superiority of our method are verified and analyzed in the BA scale-free networks.     

Robustness quantification method for network intrusion detection models

Deep learning techniques have been successfully applied to network intrusion detection tasks, but as in the case of autonomous driving and face recognition, the reliability of the system itself has become a pressing issue. Robustness is a key attribute to determine whether a deep learning system is secure and reliable, and we also choose to explore the security of intrusion detection models from a new perspective of robustness quantification. In this paper, we focus on the intrusion detection model based on long and short-term memory, and use a fine-grained linear approximation method to derive a more accurate robustness bound on the nonlinear activation function with tighter linear constraints. We can use this bound to quantitatively measure the robustness of the detection model and determine whether the model is susceptible to the influence of adversarial samples. In our experiments, we test networks with various structures on the MNIST dataset, and the results show that our proposed method can effectively deduce the robustness bounds of output elements, and has good scalability and applicability.     

Robustness and breakup of the spiral wave in a two-dimensional lattice network of neurons

The robustness and breakup of spiral wave in a two-dimensional lattice networks of neurons are investigated. The effect of small- world type connection is often simplified with local regular connection and the long-range connection with certain probability. The network effect on the development of spiral wave can be better described by local regular connection and changeable long-range connection probability than fixed long-range connection probability because the long-range probability could be changeable ...     

Vulnerability of network of networks

Our dependence on networks – be they infrastructure, economic, social or others – leaves us prone to crises caused by the vulnerabilities of these networks. There is a great need to develop new methods to protect infrastructure networks and prevent cascade of failures (especially in cases of coupled networks). Terrorist attacks on transportation networks have traumatized modern societies. With a single blast, it has become possible to paralyze airline traffic, electric power supply, ground transportation or Internet communication. How, and at which cost can one restructure the network such that it will become more robust against malicious attacks? The gradual increase in attacks on the networks society depends on – Internet, mobile phone, transportation, air travel, banking, etc. – emphasize the need to develop new strategies to protect and defend these crucial networks of communication and infrastructure networks. One example is the threat of liquid explosives a few years ago, which completely shut down air travel for days, and has created extreme changes in regulations. Such threats and dangers warrant the need for new tools and strategies to defend critical infrastructure. In this paper we review recent advances in the theoretical understanding of the vulnerabilities of interdependent networks with and without spatial embedding, attack strategies and their affect on such networks of networks as well as recently developed strategies to optimize and repair failures caused by such attacks.     

Robustness of a perturbed topological phase

We investigate the stability of the topological phase of the toric code model in the presence of a uniform magnetic field by means of variational and high-order series expansion approaches. We find that when this perturbation is strong enough, the system undergoes a topological phase transition whose first- or second-order nature depends on the field orientation. When this transition is of second order, it is in the Ising universality class except for a special line on which the critical exponent driving the closure of the gap varies continuously, unveiling a new topological universality class.     

最优的Newman-Watts网络与遍历网络的同步

在Hindmarsh-Rose神经元动力系统中研究了Newman-Watts （NW）网络的同步,给出了一些最优同步网络的拓扑结构. 数值结果表明：NW网络的同步能力主要由耦合点在耦合空间的分布决定,耦合点分布均匀的NW网络一般具有较强的同步能力;在给定连边数的情况下,可能存在多个结构不同的最优同步网络,最优同步网络具有最强的同步能力、均匀的度分布和较好的对称性,但是其对称性不一定是最好的. 最优同步网络一般是非规则网络,但在少数情况下,规则网络也有可能是最优同步网络. 提出了一种新的网络——遍历网络,该网络具有最优同步网络的特点和很强的同步能力. 关键词： Newman-Watts网络 对称度 耦合空间 同步     

Dynamics of network motifs in genetic regulatory networks

Network motifs hold a very important status in genetic regulatory networks. This paper aims to analyse the dynamical property of the network motifs in genetic regulatory networks. The main result we obtained is that the dynamical property of a single motif is very simple with only an asymptotically stable equilibrium point, but the combination of several motifs can make more complicated dynamical properties emerge such as limit cycles. The above-mentioned result shows that network motif is a stable substructure in genetic regulatory networks while their combinations make the genetic regulatory network more complicated.     

Optimal communication schemes in a complex network: From trees to bottleneck networks

The robustness of a communication scheme in a complex network may depend on the location of distinguished nodes. We collect different approaches to the idea of vulnerability and we give methods that help us to decide the good spots for the leader nodes. More specifically, we present a constructive method that yields the best location in a communication scheme for a leader node in the case that the underlying network is tree-shaped and show how it can be used for more general networks. In order to do that we consider a local approach via the bottleneck tree associated to a given node, as well as a uniform a approach by means of the so-called bottleneck network for several communication topologies.     

Geographical networks: geographical effects on network properties

Complex networks describe a wide range of systems in nature and society. Since most real systems exist in certain physical space and the distance between the nodes has influence on the connections, it is helpful to study geographical complex networks and to investigate how the geographical constrains on the connections affect the network properties. In this paper, we briefly review our recent progress on geographical complex networks with respect of statistics, modelling, robustness, and synchronizability. It has been shown that the geographical constrains tend to make the network less robust and less synchronizable. Synchronization on random networks and clustered networks is also studied.      

Geographical networks: geographical effects on network properties

Complex networks describe a wide range of systems in nature and society. Since most real systems exist in certain physical space and the distance between the nodes has influence on the connections, it is helpful to study geographical complex networks and to investigate how the geographical constrains on the connections affect the network properties. In this paper, we briefly review our recent progress on geographical complex networks with respect of statistics, modelling, robustness, and synchronizability. It has been shown that the geographical constrains tend to make the network less robust and less synchronizable. Synchronization on random networks and clustered networks is also studied.     

基于社团结构的城市地铁网络模型研究

本文运用复杂网络理论, 对我国北京、上海、广州和深圳等城市的地铁网络进行了实证研究. 分别研究了地铁网络的度分布、聚类系数和平均路径长度. 研究表明, 该网络具有高的聚类系数和短的平均路径长度, 显示小世界网络的特征, 其度分布并不严格服从幂律分布或指数分布, 而是呈多段的分布, 显示层次网络的特征. 此外, 它还具有重叠的社团结构特征. 基于实证研究的结果, 提出一种基于社团结构的交通网络模型, 并对该模型进行了模拟分析, 模拟结果表明, 该模型的模拟结果与实证研究结果相符. 此外, 该模型还能解释其他类型的复杂网络(如城市公共汽车交通网络)的网络特性. 关键词： 复杂网络 地铁网络 小世界 社团     

Entangled networks, synchronization, and optimal network topology

A new family of graphs, entangled networks, with optimal properties in many respects, is introduced. By definition, their topology is such that it optimizes synchronizability for many dynamical processes. These networks are shown to have an extremely homogeneous structure: degree, node distance, betweenness, and loop distributions are all very narrow. Also, they are characterized by a very interwoven (entangled) structure with short average distances, large loops, and no well-defined community structure. This family of nets exhibits an excellent performance with respect to other flow properties such as robustness against errors and attacks, minimal first-passage time of random walks, efficient communication, etc. These remarkable features convert entangled networks in a useful concept, optimal or almost optimal in many senses, and with plenty of potential applications in computer science or neuroscience.     

All-optical network interface from backbone networks to local area networks based on semiconductor optical amplifiers

We report on the experimental and numerical investigations of an all-optical network interface from back- bone networks to local area networks based on semiconductor optical amplifiers （SOAs）. All-optical signals at 40 Gbps with return-to-zero （RZ） format in backbone networks are demultiplexed to signals at 10 Gbps with nonreturn-to-zero （NRZ） format in local area networks. SOAs and optical band-pass filters are used in the optical interface. We study the waveform, optical spectrum, and bit error rate （BER） of the interface scheme based on the experimental and numerical simulation results. The interface technique can be used in variable length and bit-rate variable optical networks.     

Robustness of entanglement as a signature of quantum phase transitions

We investigate the critical behavior of pairwise entanglement at quantum phase transitions (QPT) in several exactly solvable spin models with noise in system control parameters. We show that the exact critical behavior will change due to noise. When the noise is not too large, pairwise entanglement is robust as a signature of QPT in some spin models.