The network model of urban subway networks with community structure
Ding Yi-Min1 , Ding Zhuo2 , Yang Chang-Ping1
1. Faculty of Physics and Electronic, Hubei University, Wuhan 430062, China;
2. School of Business Administration, South China University of Technology, Guangzhou 510640, China
Abstract 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.
Key words :
complex networks
urban subway network
small-world
community
Received: 2012-07-30
PACS:
89.75.Hc
(Networks and genealogical trees)
89.75.-k
(Complex systems)
02.50.-r
(Probability theory, stochastic processes, and statistics)
05.10.-a
(Computational methods in statistical physics and nonlinear dynamics)
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11074067).
Corresponding Authors:
丁益民
E-mail: dymhubu@sina.com
References
[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
[26]
[27]
[1]
Cai Jun, Yu Shun-Zheng. An efficient management strategy for enhancing traffic capacity in scale-free networks [J]. Acta Phys. Sin, 2013, 62(5): 058901.
[2]
Liu Jin-Liang. Research on synchronization of complex networks with random nodes [J]. Acta Phys. Sin, 2013, 62(4): 040503.
[3]
Yuan Wei-Guo, Liu Yun, Cheng Jun-Jun, Xiong Fei. Empirical analysis of microblog centrality and spread influence based on Bi-directional connection [J]. Acta Phys. Sin, 2013, 62(3): 038901.
[4]
Deng Qi-Xiang, Jia Zhen, Xie Meng-Shu, Chen Yan-Fei. Study of directed networks-based Email virus propagation model and its concussion attractor [J]. Acta Phys. Sin, 2013, 62(2): 020203.
[5]
Yu Hui, Liu Zun, Li Yong-Jun. Key nodes in complex networks identified by multi-attribute decision-making method [J]. Acta Phys. Sin, 2013, 62(2): 020204.
[6]
Li Yu-Shan, Lü Ling, Liu Ye, Liu Shuo, Yan Bing-Bing, Chang Huan, Zhou Jia-Nan. Spatiotemporal chaos synchronization of complex networks by Backstepping design [J]. Acta Phys. Sin, 2013, 62(2): 020513.
[7]
Wang Hui, Han Jiang-Hong, Deng Lin, Cheng Ke-Qing. Dynamics of rumor spreading in mobile social networks [J]. Acta Phys. Sin, 2013, 62(11): 110505.
[8]
Gao Zhong-Ke, Hu Li-Dan, Zhou Ting-Ting, Jin Ning-De. Limited penetrable visibility graph from two-phase flow for investigating flow pattern dynamics [J]. Acta Phys. Sin, 2013, 62(11): 110507.
[9]
Yin Ning, Xu Gui-Zhi, Zhou Qian. Construction and analysis of complex brain functional network under acupoint magnetic stimulation [J]. Acta Phys. Sin, 2013, 62(11): 118704.
[10]
Ren Zhuo-Ming, Liu Jian-Guo, Shao Feng, Hu Zhao-Long, Guo Qiang. Analysis of the spreading influence of the nodes with minimum K-shell value in complex networks [J]. Acta Phys. Sin, 2013, 62(10): 108902.
[11]
Liang Yi, Wang Xing-Yuan. Chaotic synchronization in complex networks with delay nodes by non-delay and delay couplings [J]. Acta Phys. Sin, 2013, 62(1): 018901.
[12]
Gao Xiang-Yun,An Hai-Zhong,Fang Wei. Research on fluctuation of bivariate correlation of time series based on complex networks theory [J]. Acta Phys. Sin, 2012, 61(9): 098902.
[13]
Wang Ya-Qi,Yang Xiao-Yuan. Study on a model of topology evolution of wireless sensor networks among cluster heads and its immunization [J]. Acta Phys. Sin, 2012, 61(9): 090202.
[14]
LÜ Ling,Liu Shuang,Zhang Xin,Zhu Jia-Bo,Shen Na,Shang Jin-Yu. Spatiotemporal chaos anti-synchronization of a complex network with different nodes [J]. Acta Phys. Sin, 2012, 61(9): 090504.
[15]
Yu Hai-Tao,Wang Jiang,Liu Chen,Che Yan-Qiu,Deng Bin,Wei Xi-Le. Stochastic resonance in coupled small-world neural networks [J]. Acta Phys. Sin, 2012, 61(6): 068702.