Exact Solution for Clustering Coefficient of Random Apollonian Networks
FANG Pin-Jie1,2** , ZHANG Duan-Ming1** , HE Min-Hua3 , JIANG Xiao-Qin2
1 School of Physics, Huazhong University of Science and Technology, Wuhan 4300742 School of Science, Naval University of Engineering, Wuhan 4300333 School of Science, Wuhan Institute of Technology, Wuhan 430073
Abstract :By means of the series method, we obtain the exact analytical solution of clustering coefficient in random Apollonian networks [Phys. Rev. E 71 (2005) 046141 ]. Our exact analytical result is identical with the simulation, whereas in the original work, there is a deviation of about 4% between their approximate analytical result and the simulation.
收稿日期: 2015-01-07
出版日期: 2015-09-02
:
89.75.-k
(Complex systems)
89.75.Fb
(Structures and organization in complex systems)
05.10.-a
(Computational methods in statistical physics and nonlinear dynamics)
[1] Watts D J and Strogatz S H 1998 Nature 393 440 [2] Barabási A L and Albert R 1999 Science 286 509 [3] Albert R and Barabási A L 2002 Rev. Mod. Phys. 74 47 [4] Costa L F, Rodrigues F A, Travieso G and Boas P R V 2007 Adv. Phys. 56 167 [5] Klemm K and Eguíluz V M 2002 Phys. Rev. E 65 036123 [6] Klemm K and Eguíluz V M 2002 Phys. Rev. E 65 057102 [7] Dorogovtsev S N, Goltsev A V and Mendes J F F 2002 Phys. Rev. E 65 066122 [8] Andrade J S, Herrmann H J, Andrade R F S and Silva L R da 2005 Phys. Rev. Lett. 94 018702 [9] Zhou T, Yan G and Wang B H 2005 Phys. Rev. E 71 046141 [10] Chen M, Yu B M, Xu P and Chen J 2007 Physica A 385 707 [11] Zhang Z Z, Gao S Y, Chen L C, Zhou S G, Zhang H J and Guan J H 2010 J. Phys. A: Math. Theor. 43 395101 [12] Xing C M and Liu F A 2010 Acta Phys. Sin. 59 1608 (in Chinese) [13] Li L and Jin Z L 2011 Chin. Phys. Lett. 28 048701 [14] Zhang J Y, Sun W G, Tong L Y and Li C P 2013 Commun. Theor. Phys. 60 375 [15] Ding Y M, Ding Z and Yang C P 2013 Acta Phys. Sin. 62 098901 (in Chinese) [16] Jing X L, Ling X, Hu M B and Shi Q 2014 Chin. Phys. Lett. 31 080504 [17] Doye J P K and Massen C P 2005 Phys. Rev. E 71 016128 [18] Andrade R F S and Herrmann H J 2005 Phys. Rev. E 71 056131 [19] Zhang Z Z, Comellas F, Fertin G and Rong L L 2006 J. Phys. A: Math. Theor. 39 1811 [20] Zhang Z Z, Rong L L and Comellas F 2006 Physica A 364 610 [21] Wu Z X, Xu X J and Wang Y H 2006 Phys. Rev. E 73 058101 [22] Zhou T, Yan G and Wang B H 2006 Phys. Rev. E 73 058102 [23] Zhang Z Z, Rong L L and Zhou S G 2006 Phys. Rev. E 74 046105 [24] Zhang Z Z, Chen L C, Zhou S G, Fang L J, Guan J H and Zou T 2008 Phys. Rev. E 77 017102 [25] Lima F W S, Moreira A A and Araújo A D 2012 Phys. Rev. E 86 056109 [26] Shi D H, Zhu S X and Liu L 2007 Physica A 381 515
[1]
. [J]. 中国物理快报, 2020, 37(6): 68701-.
[2]
. [J]. 中国物理快报, 0, (): 68701-.
[3]
. [J]. 中国物理快报, 2017, 34(5): 58902-.
[4]
. [J]. 中国物理快报, 2016, 33(05): 50502-050502.
[5]
. [J]. 中国物理快报, 2015, 32(12): 120501-120501.
[6]
. [J]. 中国物理快报, 2014, 31(08): 80503-080503.
[7]
. [J]. 中国物理快报, 2013, 30(10): 108902-108902.
[8]
. [J]. 中国物理快报, 2013, 30(9): 90202-090202.
[9]
. [J]. 中国物理快报, 2013, 30(7): 70502-070502.
[10]
. [J]. 中国物理快报, 2013, 30(5): 58901-058901.
[11]
. [J]. 中国物理快报, 2013, 30(4): 40502-040502.
[12]
. [J]. Chin. Phys. Lett., 2012, 29(12): 120505-120505.
[13]
. [J]. 中国物理快报, 2012, 29(10): 108901-108901.
[14]
LIU Xu,XIE Zheng,YI Dong-Yun**. Community Detection by Neighborhood Similarity [J]. 中国物理快报, 2012, 29(4): 48902-048902.
[15]
DUAN Wen-Qi** . Formation Mechanism of the Accumulative Magnification Effect in a Financial Time Series [J]. 中国物理快报, 2012, 29(3): 38903-038903.