Flat-head power-law, size-independent clustering, and scaling of coevolutionary scale-free networks

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.

Keywords

scale-free network / flat-head power-law / size-independent clustering / scaling relation / coevolution

References

[1] A.-L. Barabasi and R. Albert, Science, 1999, 286: 509

[2] R. Albert and A.-L. Barabasi, Rev. Mod. Phys., 2002, 74: 47

[3] S. N. Dorogovtsev and J. F. F. Mendes, Adv. Phys., 2002, 51: 1079

[4] A. Clauset, C. R. Shalizi, and M. E. J. Newman, SIAM Review, 2009, 3: 661

[5] A.-L. Barabasi, R. Albert, and H. Jeong, Physica A, 2000, 281: 69

[6] H. Jeong, B. Tombor, R. Albert, Z. N. Oltvai, and A.-L. Barabasi, Nature, 2000, 407: 651

[7] A.-L. Barabasi, H. Jeong, Z. Neda, E. Ravasz, A. Schubert, and T. Vicsek, Physica A, 2002, 311: 590

[8] E. Ravasz, A. L. Somera, D. A. Mongru, Z. N. Oltvai, and A.-L. Barabasi, Science, 2002, 297: 1551

[9] E. Ravasz and A.-L. Barabasi, Phys. Rev. E, 2003, 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

[12] B. D. Camillo, G. Toffolo, and C. Cabelli, Ann. New York Acad. Sci., 2009, 1158: 125

[13] M. E. J. Newman, Proc. Natl. Acad. Sci. USA, 2001, 98: 404.

[14] J. Masoliver, M. Montero, and G. H. Weiss, Phys. Rev. E, 2003, 67: 021112

[15] A. A. Tsonis and P. J. Roebber, Physica A, 2004, 333: 497

[16] V. M. Eguiluz, D. R. Chialvo, G. A. Cacchi, M. Baliki, and A. V. Apkarian, Phys. Rev. Lett., 2005, 94: 018102

[17] S. Song, K. D. Miller, and L. F. Abbott, Nat. Neurosci., 2000, 3: 919

[18] J. M. Montgomery and D. V. Madison, Trends Neurosci. 2004, 27: 744

[19] A. Barrat, M. Barthelemy, and A. Vespignani, Phys. Rev. Lett., 2004, 92: 228701

[20] S. Bornholdt and T. Rohlf, Phys. Rev. Lett., 2000, 84: 6114

[21] Y. B. Xie, W. X. Wang, and B. H. Wang, Phys. Rev. E, 2007, 75: 026111

[22] M. G. Zimmermann, V. M. Eguluz, and M. S. Miguel, Phys. Rev. E, 2004, 69: 065102(R)

[23] P. Holm and M. E. J. Newman, Phys. Rev. E, 2006, 74: 056108

[24] M. Liu and K. E. Bassler, Phys. Rev. E, 2006, 74: 041910

[25] C. S. Zhou and J. Kurths, Phys. Rev. Lett., 2006, 96: 164102

[26] J. M. Pacheco, A. T. Traulsen, and M. A. Nowak, Phys. Rev. Lett., 2006, 97: 258103

[27] P. Fronczak, A. Fronczak, and J. Holyst, Phys. Rev. E, 2006, 73: 046117

[28] C. P. Zhu, S. J. Xiong, Y. J. Tian, N. Li, and K. S. Jiang, Phys. Rev. Lett., 2004, 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

[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

[32] C. Meisel and T. Gross, Phys. Rev. E, 2009, 80: 061917

[33] A. L. Do, L. Rudolf, and T. Gross, New J. Phys., 2010, 12: 063023

[34] L. X. Zhong, F. Ren, T. Qiu, J. R. Xu, B. H. Chen, and C. F. Liu, Physica A, 2010, 389: 2557

[35] H. H. Jo, H. K. Lee, and H. Park, Phys. Rev. E, 2010, 81: 066108

[36] M. Li, S. G. Guan, and C. H. Lai, New J. Phys., 2010, 12: 103032

[37] B. Wu, D. Zhou, Q. Luo, L. Wang, and A. Trausen, PLOS One, 2010, 5: e11187

[38] P. Dittrich, F. Liljeros, A. Soulier, and W. Banzhaf, Phys. Rev. Lett., 2000, 84: 3205

[39] A. Soulier and T. Halpin-Healy, Phys. Rev. Lett., 2003, 90: 258103

[40] S. N. Dorogovtsev and J. F. F. Mendes, Phys. Rev. E, 2001, 63: 056125

[41] S. N. Dorogovtsev and J. F. F. Mendes, Phys. Rev. E, 2000, 62: 1842

[42] D. Braha and Y. Bar-Yam, Phys. Rev. E, 2004, 69: 016113

[43] C. R. Myers, Phys. Rev. E, 2003, 68: 046116

[44] A. Vazquez, Phys. Rev. E, 2003, 67: 056104

[45] P. Holme and B. J. Kim, Phys. Rev. E, 2002, 65: 026107

[46] T. Zhou, G. Yan, and B. H. Wang, Phys. Rev. E, 2005, 71: 046141

[47] S. L. Bu, B. H. Wang, and T. Zhou, Physica A, 2007, 374: 864

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