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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
[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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[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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