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本文运用复杂网络理论, 对我国北京、上海、广州和深圳等城市的地铁网络进行了实证研究. 分别研究了地铁网络的度分布、聚类系数和平均路径长度. 研究表明, 该网络具有高的聚类系数和短的平均路径长度, 显示小世界网络的特征, 其度分布并不严格服从幂律分布或指数分布, 而是呈多段的分布, 显示层次网络的特征. 此外, 它还具有重叠的社团结构特征. 基于实证研究的结果, 提出一种基于社团结构的交通网络模型, 并对该模型进行了模拟分析, 模拟结果表明, 该模型的模拟结果与实证研究结果相符. 此外, 该模型还能解释其他类型的复杂网络(如城市公共汽车交通网络)的网络特性.In this paper, we present the empirical investigation results for the urban subway networks in China. The results show that all the urban subway networks have high clustering coefficient and small character path length, which exhibit a small-world behavior, the degree distributions take multiplicative exponential function forms. Otherwise, these networks are hierarchically organized by overlapping cliques, which are all the globally coupled networks. To explain these results, we introduce a network model, which is in good agreement with the empirical results; in addition, this model can explain the evolutionary procedure of other networks, such as the urban bus transport networks or the film actor networks.
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Keywords:
- complex networks /
- urban subway network /
- small-world /
- community
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[1] Albert R, Barabasi A L 2002 Rev. Mod. Phys. 74 47
[2] Dorogvtsev S N, Mendes J F F 2002 Adv. Phys. 51 1079
[3] Newman M E J 2003 SIAM Rev. 45 167
[4] Boccaletti S, Latora V, Moreno Y, Chavez M, Hwang D U 2006 Physics Reports 424 175
[5] Watts D J, Strogatz S H 1998 Nature 393 440
[6] Barabási A L, Albert R 1999 Science 286 509
[7] Milo R, Shen-Orr S, Itzkovitz S, Kashan N, Chklovskii D, Alon U 2002 Science 298 824
[8] Milo R, Itzkovitz S, Kashtan N, Levitt R, Shen-Orr S, Ayzenshtat I, Sheffer M, Alon U 2004 Science 303 1538
[9] Song C, Havlim S, Makse H A 2005 Nature 433 392
[10] Palla G, Derenyi I, Farkas I, Vicsek T 2005 Nature 435 814
[11] Clauset A, Moore C, Newman M E J 2008 Nature 453 98
[12] Li W, Cai X 2004 Phy. Rev. E 69 046106
[13] Gastner M T, Newman M E J 2006 Eur. Phys. J. B 49 247
[14] Liu Hong-Kun, Zhou Tao 2007 Acta Phys. Sin. 56 0106 (in Chinese) [刘洪鲲, 周涛 2007 物理学报 56 106]
[15] Qian J H, Han D D, Ma YG 2011 Acta Phys. Sin. 60 098901 (in Chinese) [钱江海, 韩定定, 马余刚 2011 物理学报 60 098901]
[16] Sen P, Dasgupta S, Chatterjee A 2003 Phys. Rev. E 67 036106
[17] Kurant M, Thiran P 2006 Phys. Rev. Lett. 96 138701
[18] Sienkiewicz J, Holyst J A 2005 Phys. Rev. E 72 046127
[19] Chen Y Z, Li N, He D R 2007 Physica A 376 747
[20] Yang X H, Chen G, Sun B, Chen S Y, Wang W L 2011 Physica A 390 4660
[21] Ding Y M, Ding Z 2012 Int. J. Mod. Phys. B 26 1250090
[22] Latora V, Marchiori M 2002 Physica A 314 109
[23] Seaton K A, Hackett L M 2004 Physica A 339 635
[24] Domenech A 2009 Physica A 388 4658
[25] Zhang J H, Xu X M, Hong L, Wang S L, Fei Q 2011 Physica A 290 4562
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