Flat-head power-law, size-independent clustering, and scaling of coevolutionary scale-free networks
Flat-head power-law, size-independent clustering, and scaling of coevolutionary scale-free networks
Chen-ping ZHU (朱陈平)1,2 ( ), Xiao-ting LIU (刘小廷)1 , Zhi-ming GU (古志鸣)1
1. College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China; 2. Research Center for Complex System Science, Shanghai University for Science and Technology, Shanghai 200093, China
Abstract :Scale-free topology and high clustering coexist in some real networks, and keep invariant for growing sizes of the systems. Previous models could hardly give out size-independent clustering with selforganized mechanism when succeeded in producing power-law degree distributions. Always ignored, some empirical statistic results display flat-head power-law behaviors. We modify our recent coevolutionary model to explain such phenomena with the inert property of nodes to retain small portion of unfavorable links in self-organized rewiring process. Flat-head power-law and size-independent clustering are induced as the new characteristics by this modification. In addition, a new scaling relation is found as the result of interplay between node state growth and adaptive variation of connections.
Key words :
scale-free network
flat-head power-law
size-independent clustering
scaling relation
coevolution
收稿日期: 2010-07-28
出版日期: 2011-09-05
Corresponding Author(s):
Chen-ping ZHU (朱陈平),Email:chenpingzhu@yahoo.com.cn
引用本文:
. Flat-head power-law, size-independent clustering, and scaling of coevolutionary scale-free networks[J]. Frontiers of Physics, 2011, 6(3): 337-341.
Chen-ping ZHU (朱陈平), Xiao-ting LIU (刘小廷), Zhi-ming GU (古志鸣). Flat-head power-law, size-independent clustering, and scaling of coevolutionary scale-free networks. Front. Phys. , 2011, 6(3): 337-341.
链接本文:
https://academic.hep.com.cn/fop/CN/10.1007/s11467-011-0145-8
https://academic.hep.com.cn/fop/CN/Y2011/V6/I3/337
1
A.-L. Barabasi and R. Albert, Science , 1999, 286: 509 doi: 10.1126/science.286.5439.509
2
R. Albert and A.-L. Barabasi, Rev. Mod. Phys. , 2002, 74: 47 doi: 10.1103/RevModPhys.74.47
3
S. N. Dorogovtsev and J. F. F. Mendes, Adv. Phys. , 2002, 51: 1079 doi: 10.1080/00018730110112519
4
A. Clauset, C. R. Shalizi, and M. E. J. Newman, SIAM Review , 2009, 3: 661 doi: 10.1137/070710111
5
A.-L. Barabasi, R. Albert, and H. Jeong, Physica A , 2000, 281: 69 doi: 10.1016/S0378-4371(00)00018-2
6
H. Jeong, B. Tombor, R. Albert, Z. N. Oltvai, and A.-L. Barabasi, Nature , 2000, 407: 651 doi: 10.1038/35036627
7
A.-L. Barabasi, H. Jeong, Z. Neda, E. Ravasz, A. Schubert, and T. Vicsek, Physica A , 2002, 311: 590 doi: 10.1016/S0378-4371(02)00736-7
8
E. Ravasz, A. L. Somera, D. A. Mongru, Z. N. Oltvai, and A.-L. Barabasi, Science , 2002, 297: 1551 doi: 10.1126/science.1073374
9
E. Ravasz and A.-L. Barabasi, Phys. Rev. E , 2003, 67: 026112 doi: 10.1103/PhysRevE.67.026112
10
A.-L. Barabasi, E. Ravasz, and Z. Oltvai, Lecture Notes in Physics , 2003, 625: 46
11
E. Pieroni, S. de La Fuente, and van Bentem, Proteomics , 2008, 8: 799 doi: 10.1002/pmic.200700767
12
B. D. Camillo, G. Toffolo, and C. Cabelli, Ann. New York Acad. Sci. , 2009, 1158: 125 doi: 10.1111/j.1749-6632.2008.03756.x
13
M. E. J. Newman, Proc. Natl. Acad. Sci. USA , 2001, 98: 404. doi: 10.1073/pnas.021544898
14
J. Masoliver, M. Montero, and G. H. Weiss, Phys. Rev. E , 2003, 67: 021112 doi: 10.1103/PhysRevE.67.021112
15
A. A. Tsonis and P. J. Roebber, Physica A , 2004, 333: 497 doi: 10.1016/j.physa.2003.10.045
16
V. M. Eguiluz, D. R. Chialvo, G. A. Cacchi, M. Baliki, and A. V. Apkarian, Phys. Rev. Lett. , 2005, 94: 018102 doi: 10.1103/PhysRevLett.94.018102
17
S. Song, K. D. Miller, and L. F. Abbott, Nat. Neurosci. , 2000, 3: 919 doi: 10.1038/78829
18
J. M. Montgomery and D. V. Madison, Trends Neurosci . 2004, 27: 744 doi: 10.1016/j.tins.2004.10.006
19
A. Barrat, M. Barthelemy, and A. Vespignani, Phys. Rev. Lett. , 2004, 92: 228701 doi: 10.1103/PhysRevLett.92.228701
20
S. Bornholdt and T. Rohlf, Phys. Rev. Lett. , 2000, 84: 6114 doi: 10.1103/PhysRevLett.84.6114
21
Y. B. Xie, W. X. Wang, and B. H. Wang, Phys. Rev. E , 2007, 75: 026111 doi: 10.1103/PhysRevE.75.026111
22
M. G. Zimmermann, V. M. Eguluz, and M. S. Miguel, Phys. Rev. E , 2004, 69: 065102(R) doi: 10.1103/PhysRevE.69.065102
23
P. Holm and M. E. J. Newman, Phys. Rev. E , 2006, 74: 056108 doi: 10.1103/PhysRevE.74.056108
24
M. Liu and K. E. Bassler, Phys. Rev. E , 2006, 74: 041910 doi: 10.1103/PhysRevE.74.041910
25
C. S. Zhou and J. Kurths, Phys. Rev. Lett. , 2006, 96: 164102 doi: 10.1103/PhysRevLett.96.164102
26
J. M. Pacheco, A. T. Traulsen, and M. A. Nowak, Phys. Rev. Lett. , 2006, 97: 258103 doi: 10.1103/PhysRevLett.97.258103
27
P. Fronczak, A. Fronczak, and J. Holyst, Phys. Rev. E , 2006, 73: 046117 doi: 10.1103/PhysRevE.73.046117
28
C. P. Zhu, S. J. Xiong, Y. J. Tian, N. Li, and K. S. Jiang, Phys. Rev. Lett. , 2004, 92: 218702 doi: 10.1103/PhysRevLett.92.218702
29
C. P. Zhu, T. Zhou, H. J. Yang, Z. M. Gu, D. R. He, and B. H. Wang, New J. Phys. , 2008, 10: 023006 doi: 10.1088/1367-2630/10/2/023006
30
T. Gross and B. Blasius, J. R. Soc. Interface , 2008, 5: 258
31
O. Graeser, C. Xu, and P. M. Hui, Europhys. Lett. , 2009, 87: 38003 doi: 10.1209/0295-5075/87/38003
32
C. Meisel and T. Gross, Phys. Rev. E , 2009, 80: 061917 doi: 10.1103/PhysRevE.80.061917
33
A. L. Do, L. Rudolf, and T. Gross, New J. Phys. , 2010, 12: 063023 doi: 10.1088/1367-2630/12/6/063023
34
L. X. Zhong, F. Ren, T. Qiu, J. R. Xu, B. H. Chen, and C. F. Liu, Physica A , 2010, 389: 2557 doi: 10.1016/j.physa.2010.02.019
35
H. H. Jo, H. K. Lee, and H. Park, Phys. Rev. E , 2010, 81: 066108 doi: 10.1103/PhysRevE.81.066108
36
M. Li, S. G. Guan, and C. H. Lai, New J. Phys. , 2010, 12: 103032 doi: 10.1088/1367-2630/12/10/103032
37
B. Wu, D. Zhou, Q. Luo, L. Wang, and A. Trausen, PLOS One , 2010, 5: e11187 doi: 10.1371/journal.pone.0011187
38
P. Dittrich, F. Liljeros, A. Soulier, and W. Banzhaf, Phys. Rev. Lett. , 2000, 84: 3205 doi: 10.1103/PhysRevLett.84.3205
39
A. Soulier and T. Halpin-Healy, Phys. Rev. Lett. , 2003, 90: 258103 doi: 10.1103/PhysRevLett.90.258103
40
S. N. Dorogovtsev and J. F. F. Mendes, Phys. Rev. E , 2001, 63: 056125 doi: 10.1103/PhysRevE.63.056125
41
S. N. Dorogovtsev and J. F. F. Mendes, Phys. Rev. E , 2000, 62: 1842 doi: 10.1103/PhysRevE.62.1842
42
D. Braha and Y. Bar-Yam, Phys. Rev. E , 2004, 69: 016113 doi: 10.1103/PhysRevE.69.016113
43
C. R. Myers, Phys. Rev. E , 2003, 68: 046116 doi: 10.1103/PhysRevE.68.046116
44
A. Vazquez, Phys. Rev. E , 2003, 67: 056104 doi: 10.1103/PhysRevE.67.056104
45
P. Holme and B. J. Kim, Phys. Rev. E , 2002, 65: 026107 doi: 10.1103/PhysRevE.65.026107
46
T. Zhou, G. Yan, and B. H. Wang, Phys. Rev. E , 2005, 71: 046141 doi: 10.1103/PhysRevE.71.046141
47
S. L. Bu, B. H. Wang, and T. Zhou, Physica A , 2007, 374: 864 doi: 10.1016/j.physa.2006.08.048
Viewed
Full text
Abstract
Cited
Shared
Discussed