Complexity in human transportation networks: a comparative analysis of worldwide air transportation and global cargo-ship movements

We present a comparative network-theoretic analysis of the two largest global transportation networks: the worldwide air-transportation network (WAN) and the global cargo-ship network (GCSN). We show that both networks exhibit surprising statistical similarities despite significant differences in topology and connectivity. Both networks exhibit a discontinuity in node and link betweenness distributions which implies that these networks naturally segregate into two different classes of nodes and links. We introduce a technique based on effective distances, shortest paths and shortest path trees for strongly weighted symmetric networks and show that in a shortest path tree representation the most significant features of both networks can be readily seen. We show that effective shortest path distance, unlike conventional geographic distance measures, strongly correlates with node centrality measures. Using the new technique we show that network resilience can be investigated more precisely than with contemporary techniques that are based on percolation theory. We extract a functional relationship between node characteristics and resilience to network disruption. Finally we discuss the results, their implications and conclude that dynamic processes that evolve on both networks are expected to share universal dynamic characteristics.     

Local affinity in heterogeneous growing networks

In this paper we present a study of the influence of local affinity in heterogeneous preferential attachment (PA) networks. Heterogeneous PA models are a generalization of the Barabási-Albert model to heterogeneous networks, where the affinity between nodes biases the attachment probability of links. Threshold models are a class of heterogeneous PA models where the affinity between nodes is inversely related to the distance between their states. We propose a generalization of threshold models where network nodes have individual affinity functions, which are then combined to yield the affinity of each potential interaction. We analyze the influence of the affinity functions in the topological properties averaged over a network ensemble. The network topology is evaluated through the distributions of connectivity degrees, clustering coefficients and geodesic distances. We show that the relaxation of the criterion of a single global affinity still leads to a reasonable power-law scaling in the connectivity and clustering distributions under a wide spectrum of assumptions. We also show that the richer behavior of the model often exhibits a better agreement with the empirical observations on real networks.     

一种强容侵能力的无线传感器网络无标度拓扑模型研究

针对无线传感器网络无标度拓扑容侵能力差的问题,本文借助节点批量到达的Poisson网络模型,提出了一种具有容侵优化特性的无标度拓扑模型,并在构建拓扑时引入剩余能量调节因子和节点度调节因子,得到了一种幂率指数可以在(1,+∞)调节的无标度拓扑结构,并通过网络结构熵优化幂率指数,得出了具有强容侵特性的幂律指数值.实验结果表明:新的拓扑保持了无标度网络的强容错性,增强了无标度网络的容侵性,并具有较好的节能优势.     

Modelling Human Cortical Network in Real Brain Space

Highly specific structural organization is of great significance in the topology of cortical networks. We introduce a human cortical network model, taking the specific cortical structure into account, in which nodes are brain sites placed in the actual positions of cerebral cortex and the establishment of edges depends on the spatial path length rather than the linear distance. The resulting network exhibits the essential features of cortical connectivity, properties of small-world networks and multiple clusters structure. Additionally, assortative mixing is also found in this model. All of these findings may be attributed to the specific cortical architecture.     

Understanding the enhanced synchronization of delay-coupled networks with fluctuating topology

We study the dynamics of networks with coupling delay, from which the connectivity changes over time. The synchronization properties are shown to depend on the interplay of three time scales: the internal time scale of the dynamics, the coupling delay along the network links and time scale at which the topology changes. Concentrating on a linearized model, we develop an analytical theory for the stability of a synchronized solution. In two limit cases, the system can be reduced to an “effective” topology: in the fast switching approximation, when the network fluctuations are much faster than the internal time scale and the coupling delay, the effective network topology is the arithmetic mean over the different topologies. In the slow network limit, when the network fluctuation time scale is equal to the coupling delay, the effective adjacency matrix is the geometric mean over the adjacency matrices of the different topologies. In the intermediate regime, the system shows a sensitive dependence on the ratio of time scales, and on the specific topologies, reproduced as well by numerical simulations. Our results are shown to describe the synchronization properties of fluctuating networks of delay-coupled chaotic maps.     

Optimal design of virtual topology reconfiguration in WDM optical networks

Virtual topology of WDM optical networks is often designed for some specific traffic matrix to get the best network performance. When traffic demand imposed on WDM optical networks changes, the network performance may degrade and even become unacceptable. So virtual topology need to be reconfigured. In previous works, virtual topology is reconfigured to achieve the best network performance, in which a large number of lightpaths need to be set up or torn down. In this paper, we try to get a tradeoff between the network performance and traffic disruption (or implementing cost). The problem of virtual topology reconfiguration for changing traffic patterns is formulated as an optimization problem and a mixed integer linear programming (MILP) algorithm is presented. Numerical results show that a large cost reduction of reconfiguration can be achieved at the expense of network performance.     

Synchronization of networks

We study the synchronization of coupled dynamical systems on networks. The dynamics is governed by a local nonlinear oscillator for each node of the network and interactions connecting different nodes via the links of the network. We consider existence and stability conditions for both single- and multi-cluster synchronization. For networks with time-varying topology we compare the synchronization properties of these networks with the corresponding time-average network. We find that if the different coupling matrices corresponding to the time-varying networks commute with each other then the stability of the synchronized state for both the time-varying and the time-average topologies are approximately the same. On the other hand, for non-commuting coupling matrices the stability of the synchronized state for the time-varying topology is in general better than the time-average topology.      

Mesoscale and clusters of synchrony in networks of bursting neurons

We study the role of network architecture in the formation of synchronous clusters in synaptically coupled networks of bursting neurons. We give a simple combinatorial algorithm that finds the largest synchronous clusters from the network topology. We demonstrate that networks with a certain degree of internal symmetries are likely to have cluster decompositions with relatively large clusters, leading potentially to cluster synchronization at the mesoscale network level. We also address the asymptotic stability of cluster synchronization in excitatory networks of Hindmarsh-Rose bursting neurons and derive explicit thresholds for the coupling strength that guarantees stable cluster synchronization.     

Synchronization of bursting neurons: what matters in the network topology

We study the influence of coupling strength and network topology on synchronization behavior in pulse-coupled networks of bursting Hindmarsh-Rose neurons. Surprisingly, we find that the stability of the completely synchronous state in such networks only depends on the number of signals each neuron receives, independent of all other details of the network topology. This is in contrast with linearly coupled bursting neurons where complete synchrony strongly depends on the network structure and number of cells. Through analysis and numerics, we show that the onset of synchrony in a network with any coupling topology admitting complete synchronization is ensured by one single condition.     

Self-Organized Optimization of Transport on Complex Networks

We propose a self-organized optimization mechanism to improve the transport capacity of complex gradient networks.We find that,regardless of network topology,the congestion pressure can be strongly reduced by the self-organized optimization mechanism.Furthermore,the random scale-free topology is more efficient to reduce congestion compared with the random Poisson topology under the optimization mechanism.The reason is that the optimization mechanism introduces the correlations between the gradient field and the local topology of the substrate network.Due to the correlations,the cutoff degree of the gradient network is strongly reduced and the number of the nodes exerting their maximal transport capacity consumedly increases.Our work presents evidence supporting the idea that scale-free networks can efficiently improve their transport capacity by selforganized mechanism under gradient-driven transport mode.     

Hierarchical organization unveiled by functional connectivity in complex brain networks

How do diverse dynamical patterns arise from the topology of complex networks? We study synchronization dynamics in the cortical brain network of the cat, which displays a hierarchically clustered organization, by modeling each node (cortical area) with a subnetwork of interacting excitable neurons. We find that in the biologically plausible regime the dynamics exhibits a hierarchical modular organization, in particular, revealing functional clusters coinciding with the anatomical communities at different scales. Our results provide insights into the relationship between network topology and functional organization of complex brain networks.     

Quantifying information loss on chaotic attractors through recurrence networks

We propose an entropy measure for the analysis of chaotic attractors through recurrence networks which are un-weighted and un-directed complex networks constructed from time series of dynamical systems using specific criteria. We show that the proposed measure converges to a constant value with increase in the number of data points on the attractor (or the number of nodes on the network) and the embedding dimension used for the construction of the network, and clearly distinguishes between the recurrence network from chaotic time series and white noise. Since the measure is characteristic to the network topology, it can be used to quantify the information loss associated with the structural change of a chaotic attractor in terms of the difference in the link density of the corresponding recurrence networks. We also indicate some practical applications of the proposed measure in the recurrence analysis of chaotic attractors as well as the relevance of the proposed measure in the context of the general theory of complex networks.     

Evolution of networks

We review the recent rapid progress in the statistical physics of evolving networks. Interest has focused mainly on the structural properties of complex networks in communications, biology, social sciences and economics. A number of giant artificial networks of this kind have recently been created, which opens a wide field for the study of their topology, evolution, and the complex processes which occur in them. Such networks possess a rich set of scaling properties. A number of them are scale-free and show striking resilience against random breakdowns. In spite of the large sizes of these networks, the distances between most of their vertices are short - a feature known as the 'small-world' effect. We discuss how growing networks self-organize into scale-free structures, and investigate the role of the mechanism of preferential linking. We consider the topological and structural properties of evolving networks, and percolation and disease spread on these networks. We present a number of models demonstrating the main features of evolving networks and discuss current approaches for their simulation and analytical study. Applications of the general results to particular networks in nature are discussed. We demonstrate the generic connections of the network growth processes with the general problems of non-equilibrium physics, econophysics, evolutionary biology, and so on.     

Emergent criticality through adaptive information processing in boolean networks

We study information processing in populations of boolean networks with evolving connectivity and systematically explore the interplay between the learning capability, robustness, the network topology, and the task complexity. We solve a long-standing open question and find computationally that, for large system sizes N, adaptive information processing drives the networks to a critical connectivity K(c)=2. For finite size networks, the connectivity approaches the critical value with a power law of the system size N. We show that network learning and generalization are optimized near criticality, given that the task complexity and the amount of information provided surpass threshold values. Both random and evolved networks exhibit maximal topological diversity near K(c). We hypothesize that this diversity supports efficient exploration and robustness of solutions. Also reflected in our observation is that the variance of the fitness values is maximal in critical network populations. Finally, we discuss implications of our results for determining the optimal topology of adaptive dynamical networks that solve computational tasks.     

Synchronized state of coupled dynamics on time-varying networks

We consider synchronization properties of coupled dynamics on time-varying networks and the corresponding time-average network. We find that if the different Laplacians corresponding to the time-varying networks commute with each other then the stability of the synchronized state for both the time-varying and the time-average topologies are approximately the same. On the other hand for noncommuting Laplacians the stability of the synchronized state for the time-varying topology is in general better than the time-average topology.     

Blocking in wavelength-routed all-optical WDM network with or without wavelength conversion

The blocking probability in wavelength-routed all-optical networks is a very important measure of performance of the network. This blocking probability can be affected by many factors such as network topology, traffic load, number of links, algorithms employed and whether wavelength conversion is available or not. In this paper we have proposed a mathematical model to reduce the blocking probability of the WDM optical network for both wavelength convertible networks as well as for wavelength non-convertible networks. The model is can be used to evaluate the blocking performance of any network topology also it can be useful to improve its performance of the given network topology.     

Spectral reconstruction of complex networks

In this paper we study the reconstruction of a network topology from the eigenvalues of its Laplacian matrix. We introduce a simple cost function and consider the tabu search combinatorial optimization method, while comparing its performance when reconstructing different categories of networks-random, regular, small-world, scale-free and clustered-from their eigenvalues. We show that this combinatorial optimization method, together with the information contained in the Laplacian spectrum, allows an exact reconstruction of small networks and leads to good approximations in the case of networks with larger orders. We also show that the method can be used to generate a quasi-optimal topology for a network associated to a dynamic process (like in the case of metabolic or protein-protein interaction networks of organisms).     

Constructing refined null models for statistical analysis of signed networks

The establishment of effective null models can provide reference networks to accurately describe statistical properties of real-life signed networks.At present,two classical null models of signed networks(i.e.,sign and full-edge randomized models)shuffle both positive and negative topologies at the same time,so it is difficult to distinguish the effect on network topology of positive edges,negative edges,and the correlation between them.In this study,we construct three re-fined edge-randomized null models by only randomizing link relationships without changing positive and negative degree distributions.The results of nontrivial statistical indicators of signed networks,such as average degree connectivity and clustering coefficient,show that the position of positive edges has a stronger effect on positive-edge topology,while the signs of negative edges have a greater influence on negative-edge topology.For some specific statistics(e.g.,embeddedness),the results indicate that the proposed null models can more accurately describe real-life networks compared with the two existing ones,which can be selected to facilitate a better understanding of complex structures,functions,and dynamical behaviors on signed networks.     

Emergence of communities in weighted networks

Topology and weights are closely related in weighted complex networks and this is reflected in their modular structure. We present a simple network model where the weights are generated dynamically and they shape the developing topology. By tuning a model parameter governing the importance of weights, the resulting networks undergo a gradual structural transition from a module-free topology to one with communities. The model also reproduces many features of large social networks, including the "weak links" property.     

基于综合故障的无线传感器网络无标度容错拓扑模型研究

针对无线传感器网络实际应用中遇到的环境损毁和能量耗尽的问题,本文首先对网络综合故障进行建模,获取满足综合故障容忍能力和网络生命期双重需求的网络节点度和节点度上限值的取值规律,并结合由无标度特征导出的两者关系,从而求得最优节点度上限值,最终引入关于节点度上限值的适应度函数,提出了容忍环境损毁和能量耗尽综合故障的无标度容错拓扑演化模型.仿真实验结果表明,该模型演化生成的无标度拓扑对环境损毁和能量耗尽具有较好的容错性,并能够有效地延长网络生命期.