Weighted complex network analysis of travel routes on the Singapore public transportation system

The structure and properties of public transportation networks have great implications for urban planning, public policies and infectious disease control. We contribute a complex weighted network analysis of travel routes on the Singapore rail and bus transportation systems. We study the two networks using both topological and dynamical analyses. Our results provide additional evidence that a dynamical study adds to the information gained by traditional topological analysis, providing a richer view of complex weighted networks. For example, while initial topological measures showed that the rail network is almost fully connected, dynamical measures highlighted hub nodes that experience disproportionately large traffic. The dynamical assortativity of the bus networks also differed from its topological counterpart. In addition, inspection of the weighted eigenvector centralities highlighted a significant difference in traffic flows for both networks during weekdays and weekends, suggesting the importance of adding a temporal perspective missing from many previous studies.     

Markov transition probability-based network from time series for characterizing experimental two-phase flow

We generate a directed weighted complex network by a method based on Markov transition probability to represent an experimental two-phase flow. We first systematically carry out gas-liquid two-phase flow experiments for measuring the time series of flow signals. Then we construct directed weighted complex networks from various time series in terms of a network generation method based on Markov transition probability. We find that the generated network inherits the main features of the time series in the network structure. In particular, the networks from time series with different dynamics exhibit distinct topological properties. Finally, we construct two-phase flow directed weighted networks from experimental signals and associate the dynamic behavior of gas-liquid two-phase flow with the topological statistics of the generated networks. The results suggest that the topological statistics of two-phase flow networks allow quantitative characterization of the dynamic flow behavior in the transitions among different gas-liquid flow patterns.     

基于多路可视图的健康与心梗患者心电图信号复杂网络识别

可视图(visibility graph, VG)算法已被证明是将时间序列转换为复杂网络的简单且高效的方法,其构成的复杂网络在拓扑结构中继承了原始时间序列的动力学特性.目前,单维时间序列的可视图分析已趋于成熟,但应用于复杂系统时,单变量往往无法描述系统的全局特征.本文提出一种新的多元时间序列分析方法,将心梗和健康人的12导联心电图(electrocardiograph, ECG)信号转换为多路可视图,以每个导联为一个节点,两个导联构成可视图的层间互信息为连边权重,将其映射到复杂网络.由于不同人群的全连通网络表现为完全相同的拓扑结构,无法唯一表征不同个体的动力学特征,根据层间互信息大小重构网络,提取权重度和加权聚类系数,实现对不同人群12导联ECG信号的识别.为判断序列长度对识别效果的影响,引入多尺度权重度分布熵.由于健康受试者拥有更高的平均权重度和平均加权聚类系数,其映射网络表现为更加规则的结构、更高的复杂性和连接性,可以与心梗患者进行区分,两个参数的识别准确率均达到93.3%.     

Community detection with consideration of non-topological information

In a network described by a graph, only topological structure information is considered to determine how the nodes are connected by edges. Non-topological information denotes that which cannot be determined directly from topological information. This paper shows, by a simple example where scientists in three research groups and one external group form four communities, that in some real world networks non-topological information (in this example, the research group affiliation) dominates community division. If the information has some influence on the network topological structure, the question arises as to how to find a suitable algorithm to identify the communities based only on the network topology. We show that weighted Newman algorithm may be the best choice for this example. We believe that this idea is general for real-world complex networks.     

A weighted network evolution with traffic flow

In this paper, we propose a simple weighted network model that generalizes the complex network model evolution with traffic flow previously presented to investigate the relationship between traffic flow and network structure. In the model, the nodes in the network are represented by the traffic flow states, the links in the network are represented by the transform of the traffic flow states, and the traffic flow transported when performing the transform of the traffic flow states is considered as the weight of the link. Several topological features of this generalized weighted model, such as the degree distribution and strength distribution, have been numerically studied. A scaling behavior between the strength and degree s∼klogk is obtained. By introducing some constraints to the generalized weighted model, we study its subnetworks and find that the scaling behavior between the strength and degree is conserved, though the topology properties are quite sensitive to the constraints.     

基于时间序列符号化模式表征的有向加权复杂网络

时间序列复杂网络分析近些年已发展成为非线性信号分析领域的一个国际热点课题.为了能更有效地挖掘时间序列(特别是非线性时间序列)中的结构特征,同时简化时间序列分析的复杂度,提出了一种新的基于时间序列符号化结合滑窗技术模式表征的有向加权复杂网络建网方法.该方法首先按照等概率区段划分的方式将时间序列做符号化处理,结合滑窗技术确定不同时刻的符号化模式作为网络的节点;然后将待分析时间序列符号化模式的转换频次和方向作为网络连边的权重和方向,从而建立时间序列有向加权复杂网络.通过对Logistic系统不同参数设置对应的时间序列复杂网络建网测试结果表明,相比经典的可视图建网方法,本文方法的网络拓扑能更简洁、直观地展示时间序列的结构特征.进而,将本文方法应用于规则排列采集的自然风场信号分析,其网络特性指标能较准确地预测采集信号的排布规律,而可视图建网方法的网络特性指标没有任何规律性的结果.     

Estimating Topology of Discrete Dynamical Networks

In this paper, by applying Lasalle's invariance principle and some results about the trace of a matrix, we propose a method for estimating the topological structure of a discrete dynamical network based on the dynamical evolution of the network. The network concerned can be directed or undirected, weighted or unweighted, and the local dynamics of each node can be nonidentical. The connections among the nodes can be all unknown orpartially known. Finally, two examples, including a Hénon map and a central network, are illustrated to verify the theoretical results.     

能量异构的无线传感器网络加权无标度拓扑研究

针对无线传感器网络节点能耗不均和如何高效获得节点和边的负载问题,提出一种局域范围内能量异构的加权无标度拓扑演化模型.通过对节点能量与负载、能耗的关系建模,建立节点能量与点权和边权的联系,进而结合点权和加权模型给出网络的演化方式,推出点权、度和边权的幂率分布规律,最终根据网络获得的点权和边权来分析负载和能耗.仿真结果表明,提出的模型不仅能够准确计算点边的负载,而且缓解了无标度网络的节点能耗不均衡问题.     

On the topological properties of the world trade web: A weighted network analysis

This paper studies the topological properties of the World Trade Web (WTW) and its evolution over time by employing a weighted-network analysis. We show that the WTW, viewed as a weighted network, displays statistical features that are very different from those obtained by using a traditional binary-network approach. In particular, we find that: (i) the majority of existing links are associated to weak trade relationships; (ii) the weighted WTW is only weakly disassortative; (iii) countries holding more intense trade relationships are more clustered.     

Analysis of the airport network of India as a complex weighted network

Transportation infrastructure of a country is one of the most important indicators of its economic growth. Here we study the Airport Network of India (ANI) which represents India’s domestic civil aviation infrastructure as a complex network. We find that ANI, a network of domestic airports connected by air links, is a small-world network characterized by a truncated power-law degree distribution and has a signature of hierarchy. We investigate ANI as a weighted network to explore its various properties and compare them with their topological counterparts. The traffic in ANI, as in the World-wide Airport Network (WAN), is found to be accumulated on interconnected groups of airports and is concentrated between large airports. In contrast to WAN, ANI is found to be having disassortative mixing which is offset by the traffic dynamics. The analysis indicates possible mechanism of formation of a national transportation network, which is different from that on a global scale.     

Topology identification of the complex networks with non-delayed and delayed coupling

In practical situation, there exists many uncertain information in complex networks, such as the topological structures. So the topology identification is an important issue in the research of the complex networks. Based on LaSalle's invariance principle, in this Letter, an adaptive controlling method is proposed to identify the topology of a weighted general complex network model with non-delayed and delayed coupling. Finally, simulation results show that the method is effective.     

Weighted and unweighted network of amino acids within protein

The information regarding the structure of a single protein is encoded in the network of interacting amino acids considered as nodes. If any two atoms from two different amino acids (nodes) are within higher cut-off distance of London-van der Waals forces, the amino acids are considered to be linked or connected. Several atoms of any amino acids in a protein may be within the above prescribed distance of several atoms of another amino acid resulting in possible multiple links between them. These multiple links are the basis of the weight of the connectivity in a protein network. Each protein has been considered as a weighted and an unweighted network of amino acids. A total of forty nine protein structures that covers the three branches of life on earth has been analyzed and several network properties have been studied. The probability degree and strength distributions of network connectivity have been obtained. It has been observed that the average strength of amino acid node depends on its degree. The results show that the average clustering coefficient of weighted network is less than that of unweighted network. It implies that the topological clustering is generated by edges with low weights. The power-law behavior of clustering coefficients of weighted and unweighted networks as a function of degree indicates that they have signatures of hierarchy. It has also been observed that the network is of assortative type.     

Synchronization Stability in Weighted Complex Networks with Coupling Delays

Realistic networks display not only a complex topological structure, but also a heterogeneous distribution of weights in connection strengths. In addition, the information spreading through a complex network is often associated with time delays due to the finite speed of signal transmission over a distance. Hence, the weighted complex network with coupling delays have meaningful implications in real world, and resultantly gains increasing attention in various fields of science and engineering. Based on the theory of asymptotic stability of linear time-delay systems, synchronization stability of the weighted complex dynamical network with coupling delays is investigated, and simple criteria are obtained for both delay-independent and delay-dependent stabilities of synchronization states. The obtained criteria in this paper encompass the established results in the literature as special cases. Some examples are given to illustrate the theoretical results.     

An improved model for structural vulnerability analysis of power networks

Electric power networks have been studied as a typical example of real-world complex networks. Traditional models for structural vulnerability analysis appear to be all based on physical topological structure. In this paper, we depict a typical power network as a weighted graph based on electrical topology by introducing its bus admittance matrix, which embodies the important characteristics of power networks in a much more realistic structure. Furthermore, the numerical simulation for both the traditional dynamical model and the proposed electrical topological model are investigated based on the IEEE 300 bus system respectively. The comparison demonstrates that the improved model is more precise and highly efficient for the analysis of structural vulnerability of power networks.     

Complex network study of Asian Go players

Tournaments of the game of Go can be represented as a directed network in which the vertices are players and a directed link is pointing from the winner to the loser for each game. In this article, we present some interesting results for the network of Asian Go players, which is composed of 756 Go players and 9473 tournaments. It is found that the topological structure of this network displays the small-world property and a significant rich-club phenomenon where high-degree nodes are tightly interconnected. In addition, we consider the weighted version of the network, and find the weights obey power-law distributions, while the strengths follow stretched exponential distributions. The time evolution of the network structure is studied and the corresponding results discussed. The analysis of this work provides a deeper understanding for the competition network structure of Asian Go players.     

Semantic networks based on titles of scientific papers

In this paper we study the topological structure of semantic networks based on titles of papers published in scientific journals. It discusses its properties and presents some reflections on how the use of social and complex network models can contribute to the diffusion of knowledge. The proposed method presented here is applied to scientific journals where the titles of papers are in English or in Portuguese. We show that the topology of studied semantic networks are small-world and scale-free.     

Applications of Markov spectra for the weighted partition network by the substitution rule

The weighted self-similar network is introduced in an iterative way. In order to understand the topological properties of the self-similar network, we have done a lot of research in this field.Firstly, according to the symmetry feature of the self-similar network, we deduce the recursive relationship of its eigenvalues at two successive generations of the transition-weighted matrix.Then, we obtain eigenvalues of the Laplacian matrix from these two successive generations.Finally, we calculate an accurate expression for the eigentime identity and Kirchhoff index from the spectrum of the Laplacian matrix.     

Multi-directed Eulerian growing networks

We introduce and analyze a model of a multi-directed Eulerian network, that is a directed and weighted network where a path exists that passes through all the edges of the network once and only once. Networks of this type can be used to describe information networks such as human language or DNA chains. We are able to calculate the strength and degree distribution in this network and find that they both exhibit a power law with an exponent between 2 and 3. We then analyze the behavior of the accelerated version of the model and find that the strength distribution has a double slope power-law behavior. Finally we introduce a non-Eulerian version of the model and find that the statistical topological properties remain unchanged. Our analytical results are compared with numerical simulations.     

Exploring evolutionary features of directed weighted hazard network in the subway construction

A better understanding of previous accidents is an effective way to reduce the occurrence of similar accidents in the future. In this paper, a complex network approach is adopted to construct a directed weighted hazard network(DWHN) to analyze topological features and evolution of accidents in the subway construction. The nodes are hazards and accidents, the edges are multiple relationships of these nodes and the weight of edges are occurrence times of repetitive relationships. The results indicate that the DWHN possesses the property of small-world with small average path length and large clustering coefficient, indicating that hazards have better connectivity and will spread widely and quickly in the network. Moreover,the DWHN has the property of scale-free network for the cumulative degree distribution follows a power-law distribution.It makes DWHN more vulnerable to target attacks. Controlling key nodes with higher degree, strength and betweenness centrality will destroy the connectivity of DWHN and mitigate the spreading of accidents in the network. This study is helpful for discovering inner relationships and evolutionary features of hazards and accidents in the subway construction.     

Rank-based model for weighted network with hierarchical organization and disassortative mixing

In this paper, we study a rank-based model for weighted network. The evolution rule of the network is based on the ranking of node strength, which couples the topological growth and the weight dynamics. Analytically and by simulations, we demonstrate that the generated networks recover the scale-free distributions of degree and strength in the whole region of the growth dynamics parameter (α>0). Moreover, this network evolution mechanism can also produce scale-free property of weight, which adds deeper comprehension of the networks growth in the presence of incomplete information. We also characterize the clustering and correlation properties of this class of networks. It is showed that at α=1 a structural phase transition occurs, and for α>1 the generated network simultaneously exhibits hierarchical organization and disassortative degree correlation, which is consistent with a wide range of biological networks.