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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.
[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
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[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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[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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