国际石油价格复杂网络的动力学拓扑性质

为了分析国际石油价格波动的变化特征,依据粗粒化方法,将1986年1月2日至2009年11月17日美国西得克萨斯原油现货逐日离岸价格转化为由3个表示涨落字符{R,e,D}构成的102种5字串组成的价格波动状态为网络节点(即连续5天的价格波动组合),按照时间顺序连边,构建原油价格有向加权波动网络,用复杂网络拓扑结构记录原油价格波动周涨落的信息,计算网络的度与度分布、聚类系数、最短路径长度等动力学统计量.结果表明,石油价格序列的波动网络节点度与累积度分布、节点度值与秩呈幂律分布,前32个节点(模态)的节点度值比较大,且这些石油价格波动模态中都包含表示价格变化上升趋势的字符.原油价格波动网络部分节点的中介中心性能力较强,24.5%的节点承担了网络80.97%的中介中心性功能,平均路径长度2.285,距离是2和3的情况占总数的86.8%,从网络结构拓扑性质这一新的角度验证了原油价格变化的复杂特征.这些对于我们识别具有拓扑统计重要性的节点模态,理解原油价格波动的内在规律和价格变化信息的传导有一定指导意义.     

多种形式的加权广义Farey组织网络金字塔的复杂性

构建了三类确定性加权广义Farey组织的网络金字塔.理论推导并数值计算了网络金字塔的拓扑性质(度分布、平均最短路径、平均聚类系数和相称性系数等),进而将Farey序列作为网络节点的确定、随机和混合的三种权重值,以此为基础计算并拟合了三类网络金字塔的点的强度分布和边的权重分布.计算结果初步揭示了加权广义Farey组织的网络金字塔的复杂性特征,有助于了解一些实际网络的复杂性和多样性.     

与地理环境相关的中国铁路客运网拓扑结构

以中国铁路车站作为“节点”,每辆列车经过的相邻两个停靠车站之间连接一条“边”,构成有方向有权重的中国铁路客运网.首先研究了该网络的拓扑结构,包括连接度、聚集系数、最短路径和强度,结果表明中国铁路客运网的连接度分布,强度分布都是介于指数分布和幂率分布之间,是一个具有小世界性质的阶层网络.修建铁路需考虑人口分布,行政区域等因素.铁路固定设施成本高,修建完成后很难做变动,因此需考虑诸多空间地理环境对中国铁路客运网的影响,如站点的连接度和站点的相连站点之间的平均行驶距离之间的关系、车站的分布密度与人口密度的关系, 关键词： 铁路客运网 拓扑统计 小世界 地理环境     

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.     

一类权重网络的加速演化模型

采用动态形成权重网络的方法，研究了在演化过程中新增边具有加速连接情况下权重网络的拓扑特性和强度分布，给出了节点强度与度的解析表达式.分析表明，加速演化的权重模型具有明显的无标度特性.再者，只要权重网络的边权重服从某一概率分布，则在演化过程中强度择优连接与度择优连接对于网络的度分布没有影响，且与具体的概率分布无关.     

基于节点拓扑特征的中国基金公司共持网络持股行为波动相关性

选取2003—2012年期间半年度中国基金公司持上市公司股票份额面板数据为样本数据,以基金公司为节点,以同一时刻共持同一家上市公司股票关系为边,以同一时刻共持的上市公司数量为权重,构建中国基金公司共持关系结构等价加权网络(简称共持网络).结合统计物理学等方法,分析了共持网络的拓扑结构稳定性及具有不同拓扑特征值的节点随时间演变过程中与共持网络中三类节点集合持股行为波动相关性.三类节点集合分别为t-1时刻基于某一股票形成的共持关系完全连通子图节点集合(第一类节点集合)、t-1时刻共持网络中非完全连通子图的节点集合(第二类节点集合)、t时刻新进入共持网络的节点集合(第三类节点集合).分析结果显示:1)节点与第二类节点集合持股行为波动呈正相关,且相关系数随着节点集聚系数的增强而增大;2)只有当节点的度和点强度值较高时,节点与第一类和第二类节点集合的持股行为呈正相关;3)不同拓扑特征条件下的节点与第三类节点集合的持股行为均不存在波动相关性.本文提供了一个研究持股行为相关性的新思路,并为进一步研究股票市场结构等价网络及节点重要性差异提供了基础.     

关联复杂网络建模及辨识研究

运用异质耦合拆分方法和驱动-响应模型,提出关联复杂网络节点参数和拓扑结构的辨识方法.首先,研究异质关联复杂网络建模方法,进而依据网络耦合性质不同,拆分构造了两类异质关联复杂网络.然后运用驱动-响应模型、LaSalle不变原理和Gram矩阵,设计节点系统参数和拓扑参数的自适应辨识观测器.所提的观测器能在线获取网络的节点参数、不同耦合性质的拓扑参数.最后,通过数值仿真验证所提方法的有效性.     

超网络中标度律的涌现

本文构建超网络和复杂网络中统一演化模型,研究超网络无标度特性演化机理和拓扑性质.利用Poisson过程理论和连续化方法对模型进行分析,获得网络稳态平均超度分布的解析表达式.仿真实验和理论分析相符合.结果表明:随着网络规模的增大,这个动态演化网络的超度分布遵循无标度的特性.它不仅将每次增加一个新节点与若干个老节点围成一条超边的超网络模型和每次增加若干个新节点与一个老节点围成一条超边的超网络模型统一在一个模型中,而且将复杂网络中著名的无标度模型也作为我们模型的特例.     

利用邻域“结构洞”寻找社会网络中最具影响力节点

识别复杂网络中的关键节点对网络结构优化和鲁棒性增强具有十分重要的意义. 经典的关键节点测量方法在一定程度上能够辨识网络中影响力节点, 但存在一定局限性: 局部中心性测量方法仅考虑节点邻居的数目, 忽略了邻居间的拓扑关系, 不能在计算中反映邻居节点间的相互作用; 全局测量方法则由于算法本身的复杂性而不能应用于大规模社会网络的分析, 另外, 经典的关键节点测量方法也没有考虑社会网络特有的社区特征. 为高效、准确地辨识具有社区结构的社会网络中最具影响力节点, 提出了一种基于节点及其邻域结构洞的局部中心性测量方法, 该方法综合考虑了节点的邻居数量及其与邻居间的拓扑结构, 在节点约束系数的计算中同时体现了节点的度属性和“桥接”属性. 利用SIR(易感-感染-免疫)模型在真实社会网络数据上对节点传播能力进行评价后发现, 所提方法可以准确地评价节点的传播能力且具有强的鲁棒性.     

一种能耗均衡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衡问题,通过对节点生命期建模,得出节点生命期受节点剩余能量和通信距离的影响,进而将两端节点生命期作为构建拓扑时边权重的影响因子,通过边权重控制节点权重,最终得出了一种能耗均衡的无线传感器网络加权无标度拓扑模型,并理论证明了该模型的点权、边权和节点度均服从幂律分布.实验结果表明,该模型具有无标度拓扑的强容错性,并有效的均衡了网络中的节点能耗,延长了网络的生命期.     

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.     

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.     

公交车停靠诱发交通瓶颈的元胞自动机模拟

利用双车道元胞自动机模型,研究公交车停靠对道路混合交通流的影响.针对港湾式和非港湾式两种不同公交车站设置,在开放边界下模拟了公交车停靠所产生的交通瓶颈问题,给出了车辆入流概率-公交车比例相平面上的相图,区分了自由流相和拥挤相,研究了相图各区中公交车站附近的平均密度和速度分布图,比较了两种公交车站情况下的道路交通流的动力学特征.研究发现,当公交车比例较小时,与非港湾式车站相比,港湾式车站可以显著改善车站处的交通状况. 关键词： 元胞自动机 混合交通流 交通瓶颈 公交车站     

Degree and wealth distribution in a network induced by wealth

A network induced by wealth is a social network model in which wealth induces individuals to participate as nodes, and every node in the network produces and accumulates wealth utilizing its links. More specifically, at every time step a new node is added to the network, and a link is created between one of the existing nodes and the new node. Innate wealth-producing ability is randomly assigned to every new node, and the node to be connected to the new node is chosen randomly, with odds proportional to the accumulated wealth of each existing node. Analyzing this network using the mean value and continuous flow approaches, we derive a relation between the conditional expectations of the degree and the accumulated wealth of each node. From this relation, we show that the degree distribution of the network induced by wealth is scale-free. We also show that the wealth distribution has a power-law tail and satisfies the 80/20 rule. We also show that, over the whole range, the cumulative wealth distribution exhibits the same topological characteristics as the wealth distributions of several networks based on the Bouchaud-Mèzard model, even though the mechanism for producing wealth is quite different in our model. Further, we show that the cumulative wealth distribution for the poor and middle class seems likely to follow by a log-normal distribution, while for the richest, the cumulative wealth distribution has a power-law behavior.     

Characterizing traffic time series based on complex network theory

A complex network is a powerful tool to research complex systems, traffic flow being one of the most complex systems. In this paper, we use complex network theory to study traffic time series, which provide a new insight into traffic flow analysis. Firstly, the phase space, which describes the evolution of the behavior of a nonlinear system, is reconstructed using the delay embedding theorem. Secondly, in order to convert the new time series into a complex network, the critical threshold is estimated by the characteristics of a complex network, which include degree distribution, cumulative degree distribution, and density and clustering coefficients. We find that the degree distribution of associated complex network can be fitted with a Gaussian function, and the cumulative degree distribution can be fitted with an exponential function. Density and clustering coefficients are then researched to reflect the change of connections between nodes in complex network, and the results are in accordance with the observation of the plot of an adjacent matrix. Consequently, based on complex network analysis, the proper range of the critical threshold is determined. Finally, to mine the nodes with the closest relations in a complex network, the modularity is calculated with the increase of critical threshold and the community structure is detected according to the optimal modularity. The work in our paper provides a new way to understand the dynamics of traffic time series.     

Scale-Free Properties in Traffic System

In this work, we propose a new model of evolution networks, which is based on the evolution of the traffic flow. In our method, the network growth does not take into account preferential attachment, and the attachment of new node is independent of the degree of nodes. Our aim is that employing the theory of evolution network, we give a further understanding about the dynamical evolution of the traffic flow. We investigate the probability distributions and scaling properties of the proposed model. The simulation results indicate that in the proposed model, the distribution of the output connections can be well described by scale-free distribution. Moreover, the distribution of the connections is largely related to the traffic flow states, such as the exponential distribution (i.e., the scale-free distribution) and random distribution etc.     

Scale-Free Properties in Traffic System

In this work, we propose a new model of evolution networks, which is based on the evolution of the traffic flow. In our method, the network growth does not take into account preferential attachment, and the attachment of new node is independent of the degree of nodes. Our aim is that employing the theory of evolution network, we give a further understanding about the dynamical evolution of the traffic flow. We investigate the probability distributions and scaling properties of the proposed model The simulation results indicate that in the proposed model, the distribution of the output connections can be well described by scale-free distribution. Moreover, the distribution of the connections is largely related to the traffic flow states, such as the exponential distribution （i.e., the scale-free distribution） and random distribution etc.     

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.     

Road traffic: A case study of flow and path-dependency in weighted directed networks

How much can we tell about flows through networks just from their topological properties? Whereas flow distributions of river basins, trees or cardiovascular systems come naturally to mind, more complex topologies are not so immediate, especially if the network is large and heterogeneously directed. Our study is motivated by the question of how the distribution of path-dependent trails in directed networks is correlated to the distribution of network flows. As an example we have studied the path-dependencies in closed trails in four metropolitan areas in England and the USA and computed their global and spatial correlations with measured traffic flows. We have found that the heterogeneous distribution of traffic intensity is mirrored by the distribution of agglomerate path-dependency and that high traffic roads are packed along corridors at short-to-medium trail lengths from the ensemble of nodes.