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为分析公交复杂网络的拓扑性质, 本文以北京市为例, 选取截止到2010年7月的北京全市(14区、2县)的1165条公交线路和9618个公交站点为样本数据, 运用复杂网络理论构建起基于邻接站点的有向加权复杂网络模型. 该方法以公交站点作为节点, 相邻站点之间的公交线路作为边, 使得网络既具有复杂网络的拓扑性质同时节点(站点)又具有明确的地理坐标. 对网络中节点度、点强度、强度分布、平均最短路径、聚类系数等性质的分析显示, 公交复杂网络的度和点强度分布极为不均, 网络中前5%和前10%节点的累计强度分布分别达到22.43%和43.02%; 点强度与排列序数、累积强度分布都服从幂律分布, 具有无标度和小世界的网络特点, 少数关键节点在网络中发挥着重要的连接作用. 为分析复杂网络中的关键节点, 本文通过承载压力分析和基于"掠夺" 的区域中心节点提取两种方法, 得到了公交复杂网络中两类不同表现的关键节点. 这些规律也为优化城市公交网络及交通规划发展提供了新的参考建议.To analyze the topological properties of Beijing public transport network, until July 2010, we have collected 1165 bus lines and 9618 bus stops of Beijing City (14 districts and 2 counties) as the sample data to build up a directed and weighted complex network model based on neighboring stops by applying the complex network theory. In this model, bus stops are considered as nodes of the complex network, while bus lines connecting two neighboring stops as edges. Consequently, the network has the topological properties of a complex network and meanwhile the nodes (bus stops) have clear geographic coordinates. The complexity of Beijing public transport is then verified through analyzing the topological properties of node degree, node strength, strength distribution, average shortest path, clustering coefficient in the complex network. We find that the distributions of node degrees and node strengths are extremely uneven and the cumulative strength distributions of the top 5% and 10% nodes reach 22.43% and 43.02% respectively. The results also show that the node strength, ordinal number and cumulative strength distribution of the nodes all follow the power-law distribution, showing the network characteristics of scale-free and small world. Some "key nodes" play an important role in network connection. We find two kinds of "key nodes" by using high carrying pressure node analysis and extract regional central analysis. These rules provide new references for optimizing the urban transport network, managing traffic congestion and planning and developing the traffic.
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[2] Barabási A L, Albert R 1999 Science 286 509
[3] Albert R, Barabasi A L 2002 Rev. Mod. Phys . 74 47
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[9] Zhou L, Zhi R, Feng A X, Gong Z Q 2010Acta Phys. Sin. 59 6689 (in Chinese) [周磊, 支蓉, 冯爱霞, 龚志强 2010 物理学报 59 6689]
[10] Weng W G, Ni S J, Shen S F, Yuan H Y 2007 Acta Phys.Sin. 56 1938 (in Chinese) [翁文国, 倪顺江, 申世飞, 袁宏永 2007 物理学报 56 1938]
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[13] Xu X P, Hu J H, Liu F, Liu L S 2007 Phys. A 374 441
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[15] Gao Z Y, Wu J J, Mao B H, Huang H J 2005 J. Tran. Sys. Eng. & Info. Tech. 5 79 (in Chinese) [高自友, 吴建军, 毛保华, 黄海军 2005 交通运输系统工程与信息 5 79]
[16] Yook S H, Jeong H, Barabási A L, Tu Y 2001 Phys. Rev. Lett. 86 5835
[17] Song C M, Havlin S, Makse H A 2006 Nature Physics 2 275
[18] Li S B, Wu J J, Gao Z Y, Lin Y, Fu B B 2011 Acta Phys. Sin. 60 050701 (in Chinese) [李树彬, 吴建军, 高自友, 林勇, 傅白白 2011 物理学报 60 050701]
[19] Holme P 2002 Phys. Rev. E 66 036119
[20] Yin C Y, Wang B H, Wang W X, Zhou T, Yang H J 2006 Physics Letters A 351 220
[21] Zhao M 2007 Ph. D. Dissertation (Hefei: University of Science and Technology of China) (in Chinese) [赵明 2007 博士学位论文 (合肥: 中国科学技术大学)]
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[1] Watts D J, Strogatz S H 1998 Nature 393 440
[2] Barabási A L, Albert R 1999 Science 286 509
[3] Albert R, Barabasi A L 2002 Rev. Mod. Phys . 74 47
[4] Wu J S, Di Z R 2004 Prog. Phys. 24 18 (in Chinese) [吴金闪, 狄增如 2004 物理学进展 24 18]
[5] Li J, Wang B H, Jiang P Q, Zhou T, Wang W X 2006 Acta Phys. Sin. 55 4051 (in Chinese) [李季, 汪秉宏, 蒋品群, 周涛, 王文旭 2006 物理学报 55 4051]
[6] Chen Q H, Shi D H 2006 Phys. A 360 121
[7] Xu D, Li X, Wang X F 2007 Acta Phys. Sin. 56 1313 (in Chinese) [许丹, 李翔, 汪小帆 2007 物理学报 56 1313]
[8] Zhang L, Liu Y 2008 Acta Phys. Sin. 57 5419 (in Chinese) [张立, 刘云 2008 物理学报 57 5419]
[9] Zhou L, Zhi R, Feng A X, Gong Z Q 2010Acta Phys. Sin. 59 6689 (in Chinese) [周磊, 支蓉, 冯爱霞, 龚志强 2010 物理学报 59 6689]
[10] Weng W G, Ni S J, Shen S F, Yuan H Y 2007 Acta Phys.Sin. 56 1938 (in Chinese) [翁文国, 倪顺江, 申世飞, 袁宏永 2007 物理学报 56 1938]
[11] Marco A J, Brian H W, Jenny L, 2000 Nick Abel Ecological Modelling 131 249
[12] Vamsi K, Vishal S, Aaron C, Cristopher M 2006 arXiv:0510198
[13] Xu X P, Hu J H, Liu F, Liu L S 2007 Phys. A 374 441
[14] Zhou S, Mondragon R J 2004 arXiv:0308036
[15] Gao Z Y, Wu J J, Mao B H, Huang H J 2005 J. Tran. Sys. Eng. & Info. Tech. 5 79 (in Chinese) [高自友, 吴建军, 毛保华, 黄海军 2005 交通运输系统工程与信息 5 79]
[16] Yook S H, Jeong H, Barabási A L, Tu Y 2001 Phys. Rev. Lett. 86 5835
[17] Song C M, Havlin S, Makse H A 2006 Nature Physics 2 275
[18] Li S B, Wu J J, Gao Z Y, Lin Y, Fu B B 2011 Acta Phys. Sin. 60 050701 (in Chinese) [李树彬, 吴建军, 高自友, 林勇, 傅白白 2011 物理学报 60 050701]
[19] Holme P 2002 Phys. Rev. E 66 036119
[20] Yin C Y, Wang B H, Wang W X, Zhou T, Yang H J 2006 Physics Letters A 351 220
[21] Zhao M 2007 Ph. D. Dissertation (Hefei: University of Science and Technology of China) (in Chinese) [赵明 2007 博士学位论文 (合肥: 中国科学技术大学)]
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