Empirical analysis of a scale-free railway network in China

We present a detailed, empirical analysis of the statistical properties of the China Railway Network (CRN) consisting of 3915 nodes (train stations) and 22 259 edges (railways). Based on this, CRN displays two explicit features already observed in numerous real-world and artificial networks. One feature, the small-world property, has the fingerprint of a small characteristic shortest-path length, 3.5, accompanied by a high degree of clustering, 0.835. Another feature is characterized by the scale-free distributions of both degrees and weighted degrees, namely strengths. Correlations between strength and degree, degree and degree, and clustering coefficient and degree have been studied and the forms of such behaviors have been identified. In addition, we investigate distributions of clustering coefficients, topological distances, and spatial distances.     

Empirical analysis of the worldwide maritime transportation network

In this paper we present an empirical study of the worldwide maritime transportation network (WMN) in which the nodes are ports and links are container liners connecting the ports. Using the different representations of network topology — the spaces L and P, we study the statistical properties of WMN including degree distribution, degree correlations, weight distribution, strength distribution, average shortest path length, line length distribution and centrality measures. We find that WMN is a small-world network with power law behavior. Important nodes are identified based on different centrality measures. Through analyzing weighted clustering coefficient and weighted average nearest neighbors degree, we reveal the hierarchy structure and rich-club phenomenon in the network.     

Empirical analysis of the evolution of a scientific collaboration network

We present an analysis of the temporal evolution of a scientific coauthorship network, the genetic programming network. We find evidence that the network grows according to preferential attachment, with a slightly sublinear rate. We empirically find how a giant component forms and develops, and we characterize the network by several other time-varying quantities: the mean degree, the clustering coefficient, the average path length, and the degree distribution. We find that the first three statistics increase over time in the growing network; the degree distribution tends to stabilize toward an exponentially truncated power-law. We finally suggest an effective network interpretation that takes into account the aging of collaboration relationships.     

Empirical analysis of dependence between stations in Chinese railway network

A railway transportation system can be represented by a bipartite network consisting of trains and stations, where a train is connected to all stations where it stops. In this paper, motivated by the resource-allocation process taking place on networks, we design a method to project a Chinese train-station bipartite network into a weighted station network. A new metric is proposed to quantify the dependence between pairs of stations, which is shown to follow a shifted power-law distribution. In addition, we compare the resource-allocation method and the well-known multiple-edge method, and the results indicate that our proposed method is more reasonable.     

Geographic coarse graining analysis of the railway network of China

We investigate the detailed, empirical analysis of the statistical properties of the Railway Network of China (RNC) in space L and space G, constructed by geographic coarse graining process. The RNC exhibits similar properties in the cumulative distributions of degree and strength in two spaces, and it presents the hierarchical structure, small-world behavior and assortativity, areciprocal connection both in space L and space G. We also investigate the path length that every train runs, the distribution of the railroad length per degree and the optimal distribution of stations.     

Networked analysis of the Shanghai subway network,in China

Recently, cities have become larger and larger, and more and more people are living in large cities. This phenomenon has caused serious traffic congestion which is very detrimental to the development of large cities. In this context, the subway has become the most effective solution for relieving traffic congestion and subways have been constructed in many cities, so the reliability and robustness of subways should be guaranteed. In this paper, Shanghai subway network, in China, will be analyzed and investigated; the topological characteristics and functional properties can be studied in order to assess the reliability and robustness. The topological characteristics can be measured using several parameters; meanwhile the fraction of removed nodes of Shanghai subway network is discussed and compared against that for a random network, and the critical threshold of this fraction is obtained. Two novel parameters called the functionality loss and connectivity of subway lines are proposed for measuring the transport functionality and the connectivity of subway lines. Subway lines 4 and 7 are selected as examples for evaluating the connectivity of lines subjected to different attack protocols. This study indicates that the subway network is robust against random attacks but fragile for malicious attacks, and the highest betweenness node-based attacks can cause the most serious damage to subway networks among the different attack protocols.     

Empirical investigation of topological and weighted properties of a bus transport network from China

Many bus transport networks(BTNs) have evolved into directed networks. A new representation model for BTNs is proposed, called directed-space P. The bus transport network of Harbin(BTN-H) is described as a directed and weighted complex network by the proposed representation model and by giving each node weights. The topological and weighted properties are revealed in detail. In-degree and out-degree distributions, in-weight and out-weight distributions are presented as an exponential law, respectively. There is a strong relation between in-weight and in-degree(also between out-weight and out-degree), which can be fitted by a power function. Degree–degree and weight–weight correlations are investigated to reveal that BTN-H has a disassortative behavior as the nodes have relatively high degree(or weight). The disparity distributions of out-degree and in-degree follow an approximate power-law. Besides, the node degree shows a near linear increase with the number of routes that connect to the corresponding station. These properties revealed in this paper can help public transport planners to analyze the status quo of the BTN in nature.     

中国城市航空网络的实证研究与分析

以城市为节点，城市间直航线路为边，实证地研究了中国城市航空网络的拓扑性质.研究表明，中国城市航空网络是一个小世界网络，具有短的平均路径长度和大的簇系数，且其度分布服从双段幂律分布.它的度度相关性质与世界航空网络和北美航空网络都不相同.当度较小时，世界航空网络和北美航空网络都是正相关的，但中国城市航空网络未表现出度度相关性；而对于度较大的节点，世界航空网络中其邻点平均度几乎是一个常值，但中国城市航空网络却呈现出负相关性.以往的实证研究暗示，节点具有明确几何位置的网络，如计算机互联网、电力网络等，不表现层次性.但是中国城市航空网络展现出明显的层次性，表明地理因素对其结构演化的影响并不强烈.进一步地，以城市间直航计划每周提供的座位数为边权，研究了网络的含权性质，发现该网络节点度权之间是幂律相关的，相关指数为1.37.     

Empirical extraction of mechanisms underlying real world network generation

The generation mechanisms of real world networks have been described using multiple models. The mathematical features of these models are usually extrapolated from statistical properties of a snapshot of these networks. We here propose an alternative method based on direct measurement of a sequence of consecutive snapshots to uncover the dynamics underlying real world generation. We assume that the probability of adding a node or an edge depends only on local features surrounding the newly added node/edge, and directly measure the contribution of these features to the node/edge addition probability. These measurements are performed using newly defined N-node local structures. Each N-node local structure represents the configuration of edges surrounding a newly added edge. The N-node local structure measurements reproduce for some networks the now classical addition of edges between high degree node mechanisms. It also provides quantitative estimates of more complex mechanisms driving other networks’ evolution, such as the effect of common first and second neighbors. This new methodology reveals the relative importance of different generation mechanisms. We show, for example, that the main mechanism driving hyperlink addition between two websites is the existence of a third website linking to both the source and the target of the new hyperlink.     

Empirical analysis of online human dynamics

Patterns of human activities have attracted increasing academic interests, since the quantitative understanding of human behavior is helpful to uncover the origins of many socioeconomic phenomena. This paper focuses on behaviors of Internet users. Six large-scale systems are studied in our experiments, including the movie-watching in Netflix and MovieLens, the transaction in Ebay, the bookmark-collecting in Delicious, and the posting in FreindFeed and Twitter. Empirical analysis reveals some common statistical features of online human behavior: (1) The total number of user’s actions, the user’s activity, and the interevent time all follow heavy-tailed distributions. (2) There exists a strongly positive correlation between user’s activity and the total number of user’s actions, and a significantly negative correlation between the user’s activity and the width of the interevent time distribution. We further study the rescaling method and show that this method could to some extent eliminate the different statistics among users caused by the different activities, yet the effectiveness depends on the data sets.     

Visibility graph analysis on quarterly macroeconomic series of China based on complex network theory

The visibility graph approach and complex network theory provide a new insight into time series analysis. The inheritance of the visibility graph from the original time series was further explored in the paper. We found that degree distributions of visibility graphs extracted from Pseudo Brownian Motion series obtained by the Frequency Domain algorithm exhibit exponential behaviors, in which the exponential exponent is a binomial function of the Hurst index inherited in the time series. Our simulations presented that the quantitative relations between the Hurst indexes and the exponents of degree distribution function are different for different series and the visibility graph inherits some important features of the original time series. Further, we convert some quarterly macroeconomic series including the growth rates of value-added of three industry series and the growth rates of Gross Domestic Product series of China to graphs by the visibility algorithm and explore the topological properties of graphs associated from the four macroeconomic series, namely, the degree distribution and correlations, the clustering coefficient, the average path length, and community structure. Based on complex network analysis we find degree distributions of associated networks from the growth rates of value-added of three industry series are almost exponential and the degree distributions of associated networks from the growth rates of GDP series are scale free. We also discussed the assortativity and disassortativity of the four associated networks as they are related to the evolutionary process of the original macroeconomic series. All the constructed networks have “small-world” features. The community structures of associated networks suggest dynamic changes of the original macroeconomic series. We also detected the relationship among government policy changes, community structures of associated networks and macroeconomic dynamics. We find great influences of government policies in China on the changes of dynamics of GDP and the three industries adjustment. The work in our paper provides a new way to understand the dynamics of economic development.     

Statistical analysis of the road network of India

In this paper we study the Indian highway network as a complex network where the junction points are considered as nodes, and the links are formed by an existing connection. We explore the topological properties and community structure of the network. We observe that the Indian highway network displays small-world properties and is assortative in nature. We also identify the most important road-junctions (or cities) in the highway network based on the betweenness centrality of the node. This could help in identifying the potential congestion points in the network. Our study is of practical importance and could provide a novel approach to reduce congestion and improve the performance of the highway network.     

A network analysis of the Chinese stock market

In many practical important cases, a massive dataset can be represented as a very large network with certain attributes associated with its vertices and edges. Stock markets generate huge amounts of data, which can be use for constructing the network reflecting the market’s behavior. In this paper, we use a threshold method to construct China’s stock correlation network and then study the network’s structural properties and topological stability. We conduct a statistical analysis of this network and show that it follows a power-law model. We also detect components, cliques and independent sets in this network. These analyses allows one to apply a new data mining technique of classifying financial instruments based on stock price data, which provides a deeper insight into the internal structure of the stock market. Moreover, we test the topological stability of this network and find that it displays a topological robustness against random vertex failures, but it is also fragile to intentional attacks. Such a network stability property would be also useful for portfolio investment and risk management.     

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.     

梯形网络等效电阻的网络分析

基于A参数，利用网络分析法，得到了梯形网络等效电阻的一般表达式，并将结果与相关讨论进行了比较。     

Empirical analysis on a keyword-based semantic system

Keywords in scientific articles have found their significance in information filtering and classification. In this article, we empirically investigated statistical characteristics and evolutionary properties of keywords in a very famous journal, namely Proceedings of the National Academy of Science of the United States of America (PNAS), including frequency distribution, temporal scaling behavior, and decay factor. The empirical results indicate that the keyword frequency in PNAS approximately follows a Zipf’s law with exponent 0.86. In addition, there is a power-low correlation between the cumulative number of distinct keywords and the cumulative number of keyword occurrences. Extensive empirical analysis on some other journals’ data is also presented, with decaying trends of most popular keywords being monitored. Interestingly, top journals from various subjects share very similar decaying tendency, while the journals of low impact factors exhibit completely different behavior. Those empirical characters may shed some light on the in-depth understanding of semantic evolutionary behaviors. In addition, the analysis of keyword-based system is helpful for the design of corresponding recommender systems.     

Empirical analysis of picosecond breakdown in sulfur hexafluoride

Using state of the art equipment and multiple simultaneous data acquisition systems, breakdown in sulfur hexafluoride (SF₆) is examined in high resolution. Recorded risetimes can be as fast as 50 ps. Influential parameters of breakdown are identified, recorded, and categorized. Methods for removing the impact of the measurement system are implemented in efforts to distinguish the physical phenomenon from influential external factors. Observed waveforms and breakdown characteristics are categorized into three types. Each type is particular to a specific parameter range – i.e. electric field E/p or the product of pressure and distance pd.     

Empirical analysis of quantum finance interest rates models

Empirical forward interest rates drive the debt markets. Libor and Euribor futures data is used to calibrate and test models of interest rates based on the formulation of quantum finance. In particular, all the model parameters, including interest rate volatilities, are obtained from market data. The random noise driving the forward interest rates is taken to be a Euclidean two dimension quantum field. We analyze two models, namely the bond forward interest rates, which is a linear theory and the Libor Market Model, which is a nonlinear theory. Both the models are analyzed using Libor and Euribor data, with various approximations to match the linear and nonlinear models. The results are quite good, with the linear model having an accuracy of about 99% and the nonlinear model being slightly less accurate. We extend our analysis by directly using the Zero Coupon Yield Curve (ZCYC) data for Libor and for bonds; but due to some technical difficulties we could not derive the models parameters directly from the ZCYC data.     

准方波脉冲形成网络的理论分析与设计

针对微波驱动源、固态调制器等对宽平顶脉冲源的应用需求,开展了基于脉冲形成网络输出准方波的理论研究与分析设计。首先采用Prony算法获得准方波波形的解析表达式,然后基于最佳一致逼近的优化控制思路,列出极点控制方程,采用数值方法求解非线性方程组,获得优化波形参数。在此基础上采用阻抗函数匹配的算法求解出脉冲形成网络的元件参数初始值,根据工程设计的实际情况舍弃部分参数并对个别参数进行优化后,获得最终的元器件参数。通过理论分析与数值模拟相结合的方法,系统地给出了获取长脉宽、低纹波准方波脉冲形成网络的设计方法以及设计准则。该方法可用于设计任意阶低纹波系数的准方波脉冲源,也可用于设计其他输出波形要求的脉冲源。