北京市地铁网络拓扑结构复杂性研究  

Study on the complexity of Beijing metro network

作　　者：张晋[1] 梁青槐[1] 贺晓彤 

机构地区：[1]北京交通大学城市轨道交通研究中心,北京100044

出　　处：《北京交通大学学报》2013年第6期78-84,共7页JOURNAL OF BEIJING JIAOTONG UNIVERSITY

基　　金：国家"十一五"科技支撑项目资助(2006BAJ18B04-07)

摘　　要：针对北京市地铁实际网络及运营关系,分别构建了SpaceL和SpaceP拓扑结构模型.基于复杂网络理论,应用现有和新的特征统计指标对两种不同的拓扑结构模型复杂性进行了分析.对SpaceL模型的研究显示,其节点度符合指数为4.1的幂律分布,满足无标度特性;其网络平均距离为15.26,连通度为0.36,代表容错性的补图效率为96.7%,说明其具备小世界网络短距离、高容错性的特点,但不同节点的补图效率显示,少量hub节点的故障会对网络造成较大损失,需重点防护.对SpaceP模型的研究显示,其网络度分布同样具有"幂律结尾"的无标度特性,幂指数为4.2;其平均距离为2.68,小于网络规模的对数(5.2),聚类系数达到0.94,具有明显的小世界特征.研究表明无论是实际网络还是运营层面上,地铁线网都具有复杂网络特征,这对进一步研究地铁线网的结构特性具有启示作用.According to the physical structure and operating characteristics, the paper builds the SpaceL and SpaceP topology mode of Beijing metro network. Based on the complex network theory, we use new and existing statistical indicators to analyze the above models. For SpaceL model, the vertex con- nectivity follows a scale-free distribution with a power-law exponent as 4.1, which shows that it is a scale-free network. As a planar network, it has a characteristic path length of 15.26, a degree of con- nectivity is 0.36, and the complement efficiency which represents fault tolerance as high as 96.7 %. All those results demonstrate that SpaceL model of Beijing metro is a small-world network. However, the fault tolerance of vertices indicates there are a few hubs which are critical to the stability of the net- work. For SpaceP model, the distribution of vertex degree also has a power-law tail with a exponent as 4.2. It has a characteristic path length of 2.68, which is lower than the logarithm of the network size （5.2）, and the clustering coefficient up to 0.94, which indicates that SpaceP model of Beijing metro is a small-world network. Finally, we find that no matter in terms of spatial structure or operational lev- el, the metro network has complex network characteristics, which is enlightening for further revealing the network properties of metro system.

关 键 词：北京地铁 复杂网络 无标度特性 小世界特性 容错性 网络效率 

分 类 号：U231[交通运输工程—道路与铁道工程]