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提出复杂网络的另一类家族的确定性金字塔，它是由确定性的不同连接方式构造的广义Farey组织的网络金字塔(GFONP)，理论推导了该类金字塔网络的拓扑性质及其转变特点，发现三种GFONP网络的度分布都服从指数分布形式，随着时间t的不断演化网络金字塔群聚系数不断减小并趋于一个常数，同时网络金字塔从异配向同配转变，度-度相关系数也趋于一个正的常数. 结果显示这类型网络的新特性具有应用潜力.
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关键词:
- 广义Farey组织网络金字塔 /
- 复杂网络 /
- 网络特性
Another family of complex network—— the generalized Farey organized network pyramid (GFONP) is introduced. Three typical determinate constructional algorithms are shown, and corresponding topological characteristics are studied by theoretical and numerical analysis. The results show that the three determinate GFOPN networks have similar characteristics, i.e. their degree distributions follow exponential distribution in form, the clustering coefficient of the network decreases to a constant value with the step t increasing, the resulting network evolves from one with disassortative to one with assortative coefficient with increasing t, and the degree-degree correlation coefficient tends to a positive constant. This may lead to potential applications of the network of pyramidal structure.[1] ［1］Watts D J, Strogatz S H 1998 Nature 393 440
[2] ［2］Barabási A L, Albert R 1999 Science 286 509
[3] ［3］Fang J Q, Wang X F, Zheng Z G, Bi Q, Di Z R, LI X 2007 Progress in Physics 27 239(in Chinese) ［方锦清、汪小帆、郑志刚、毕桥、狄增如、李翔 2007 物理学进展 27 239］
[4] ［4］Fang J Q, Wang X F, Zheng Z G, LI X, Di Z R, Bi Q 2007 Progress in Physics 27 361(in Chinese) ［方锦清、汪小帆、郑志刚、李翔、狄增如、毕桥 2007 物理学进展 27 361］
[5] ［5］Fang J Q 2008 Mastering Beam Halo and Exploring Network Science (Beijing: Atomic Energy Press)p57 (in Chinese) ［方锦清 2008 驾驭强流束晕与探索网络科学（北京：原子能出版社）第57页］
[6] ［6］Chen G R, Xu X M 2008 Complex Networks Theory and Applications(Hong Kong: Shanghai Systems Science Press) p1 (in Chinese) ［陈关荣、徐晓鸣 2008 复杂网络理论与应用（香港：上海系统科学出版社）第1页］
[7] ［7］Wang X F, Li X, Chen G R 2006 Complex Network theory and Its Application (Beijing: Tsinghua University Press) p18 (in Chinese) ［汪小帆、李翔、陈关荣 2006 复杂网络理论及其应用（北京：清华大学出版社）第18页］
[8] ［8］He D R, Liu Z H, Wang B H 2009 Complex systems and complex networks (Beijing: Higher Education Press) p1 (in Chinese) ［何大韧、刘宗华、汪秉宏2009复杂系统与复杂网络（北京：高等教育出版社）第1页］
[9] ［9］He Y, Zhang P P, Xu T, Jiang Y M, He D R 2004 Acta Phys. Sin. 53 1710 (in Chinese) ［何阅、张培培、许田、姜玉梅、何大韧 2004 53 1710］
[10] ］Li J, Wang B H, Jiang P Q, Zhou T, Wang W X 2006 Acta Phys. Sin. 55 4051 (in Chinese) ［李季、汪秉宏、蒋品群、周涛、王文旭 2006 55 4051］
[11] ］Wang Y, Zheng Z G 2009 Acta Phys. Sin. 58 4421(in Chinese) ［王延、郑志刚 2009 58 4421］
[12] ］Fang J Q, Liang Y 2005 Chin. Phys. Lett. 22 2719
[13] ］Fang J Q, Bi Q, Li Y, Lu X B, Liu Q 2007 Advances in Complex Systems 10 117
[14] ］Fang J Q, Li Y, Bi Q 2007 International Journal of Modern Physics B 2130 5121
[15] ］Li Y, Fang J Q, Liu Q, Liang Y 2006 Commun. Theor. Phys. 45 67
[16] ］Fang J Q, Bi Q, Li Y, Lu X B, Liu Q 2007 Chin. Phys. Lett. 24 279
[17] ］Fang J Q, Bi Q, Li Y, Lu X B, Liu Q 2007 Chinese Science 50 379
[18] ］Fang J Q, Bi Q, Li Y, Lu X B, Liu Q 2007 Commun. Theor. Phys. 48 377
[19] ］Fang J Q, Bi Q, Li Y 2007 Science Frontiers of Physics in China 1 109
[20] ］Li Y, Fang J Q, Liu Q 2007 Entropy 9 73
[21] ］Li Y, Fang J Q, Liu Q 2007 Science & Technology Review 25 23(in Chinese) ［李永、方锦清、刘强 2007 科技导报 25 23］
[22] ］Fang J Q, Li Y, Bi Q 2008 Complex Systems and Complexity Science 5 56 (in Chinese) ［方锦清、李永、毕桥 2008 复杂系统与复杂性科学 5 56］
[23] ］Fang J Q, Li Y 2008 Advances in Mechanics 38 663 (in Chinese) ［方锦清、李永 2008 力学进展 38 663］
[24] ］Fang J Q 2009 Int. J. Systems 1 453
[25] ］Fang J Q, Li Y 2009 First International Conference, Complex 2009 (Berlin：Springer) p78
[26] ］Fang J Q, Wang X F, Zheng Z G 2009 Progress in Physics 29 1 (in Chinese) ［方锦清、汪小帆、郑志刚 2009 物理学进展 29 1］
[27] ］Fang J Q, Li Y 2010 Commun.Theor.Phys. 53 389
[28] ］González M C, Barabási A L 2007 Nature Physics 3 224
[29] ］Kim S H, Ostlund S 1986 Phys. Rev. A 34 3426
[30] ］Maselko J, Swinney H L 1987 Phys. Lett. A 119 403
[31] ］Fang J Q 1990 Phys. Lett. A 146 35
[32] ］Calvo O, Cartwright J H E, Gonzalez D L, Piro O, Sportolari F 2000 IEEE Transactions 47 491
[33] ］Buchleitner A, d’Arcy M B, Fishman S, SA Gardiner, Guarneri I 2006 Phys. Rev. Lett. 96 164101
[34] ］Fang J Q, Li Y 2009 First International Conference, Complex 2009 (Berlin：Springer) p1678
[35] ］Li Y, Fang J Q, Liu Q 2009 Journal of Systems Science and Complexity (to be published)
[36] ］Liu Q, Fang J Q, Li Y Acta Phys.Sin. (in Chinese)(in Press) (Accepted)［刘强、方锦清、李永 (已接受)］
[37] ］Liu F, Cao P J, Zhang H R, Tian J F, Xiao C W, Shen C M, Li J Q, Gao H J 2005 Advanced materials 17 1893
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[1] ［1］Watts D J, Strogatz S H 1998 Nature 393 440
[2] ［2］Barabási A L, Albert R 1999 Science 286 509
[3] ［3］Fang J Q, Wang X F, Zheng Z G, Bi Q, Di Z R, LI X 2007 Progress in Physics 27 239(in Chinese) ［方锦清、汪小帆、郑志刚、毕桥、狄增如、李翔 2007 物理学进展 27 239］
[4] ［4］Fang J Q, Wang X F, Zheng Z G, LI X, Di Z R, Bi Q 2007 Progress in Physics 27 361(in Chinese) ［方锦清、汪小帆、郑志刚、李翔、狄增如、毕桥 2007 物理学进展 27 361］
[5] ［5］Fang J Q 2008 Mastering Beam Halo and Exploring Network Science (Beijing: Atomic Energy Press)p57 (in Chinese) ［方锦清 2008 驾驭强流束晕与探索网络科学（北京：原子能出版社）第57页］
[6] ［6］Chen G R, Xu X M 2008 Complex Networks Theory and Applications(Hong Kong: Shanghai Systems Science Press) p1 (in Chinese) ［陈关荣、徐晓鸣 2008 复杂网络理论与应用（香港：上海系统科学出版社）第1页］
[7] ［7］Wang X F, Li X, Chen G R 2006 Complex Network theory and Its Application (Beijing: Tsinghua University Press) p18 (in Chinese) ［汪小帆、李翔、陈关荣 2006 复杂网络理论及其应用（北京：清华大学出版社）第18页］
[8] ［8］He D R, Liu Z H, Wang B H 2009 Complex systems and complex networks (Beijing: Higher Education Press) p1 (in Chinese) ［何大韧、刘宗华、汪秉宏2009复杂系统与复杂网络（北京：高等教育出版社）第1页］
[9] ［9］He Y, Zhang P P, Xu T, Jiang Y M, He D R 2004 Acta Phys. Sin. 53 1710 (in Chinese) ［何阅、张培培、许田、姜玉梅、何大韧 2004 53 1710］
[10] ］Li J, Wang B H, Jiang P Q, Zhou T, Wang W X 2006 Acta Phys. Sin. 55 4051 (in Chinese) ［李季、汪秉宏、蒋品群、周涛、王文旭 2006 55 4051］
[11] ］Wang Y, Zheng Z G 2009 Acta Phys. Sin. 58 4421(in Chinese) ［王延、郑志刚 2009 58 4421］
[12] ］Fang J Q, Liang Y 2005 Chin. Phys. Lett. 22 2719
[13] ］Fang J Q, Bi Q, Li Y, Lu X B, Liu Q 2007 Advances in Complex Systems 10 117
[14] ］Fang J Q, Li Y, Bi Q 2007 International Journal of Modern Physics B 2130 5121
[15] ］Li Y, Fang J Q, Liu Q, Liang Y 2006 Commun. Theor. Phys. 45 67
[16] ］Fang J Q, Bi Q, Li Y, Lu X B, Liu Q 2007 Chin. Phys. Lett. 24 279
[17] ］Fang J Q, Bi Q, Li Y, Lu X B, Liu Q 2007 Chinese Science 50 379
[18] ］Fang J Q, Bi Q, Li Y, Lu X B, Liu Q 2007 Commun. Theor. Phys. 48 377
[19] ］Fang J Q, Bi Q, Li Y 2007 Science Frontiers of Physics in China 1 109
[20] ］Li Y, Fang J Q, Liu Q 2007 Entropy 9 73
[21] ］Li Y, Fang J Q, Liu Q 2007 Science & Technology Review 25 23(in Chinese) ［李永、方锦清、刘强 2007 科技导报 25 23］
[22] ］Fang J Q, Li Y, Bi Q 2008 Complex Systems and Complexity Science 5 56 (in Chinese) ［方锦清、李永、毕桥 2008 复杂系统与复杂性科学 5 56］
[23] ］Fang J Q, Li Y 2008 Advances in Mechanics 38 663 (in Chinese) ［方锦清、李永 2008 力学进展 38 663］
[24] ］Fang J Q 2009 Int. J. Systems 1 453
[25] ］Fang J Q, Li Y 2009 First International Conference, Complex 2009 (Berlin：Springer) p78
[26] ］Fang J Q, Wang X F, Zheng Z G 2009 Progress in Physics 29 1 (in Chinese) ［方锦清、汪小帆、郑志刚 2009 物理学进展 29 1］
[27] ］Fang J Q, Li Y 2010 Commun.Theor.Phys. 53 389
[28] ］González M C, Barabási A L 2007 Nature Physics 3 224
[29] ］Kim S H, Ostlund S 1986 Phys. Rev. A 34 3426
[30] ］Maselko J, Swinney H L 1987 Phys. Lett. A 119 403
[31] ］Fang J Q 1990 Phys. Lett. A 146 35
[32] ］Calvo O, Cartwright J H E, Gonzalez D L, Piro O, Sportolari F 2000 IEEE Transactions 47 491
[33] ］Buchleitner A, d’Arcy M B, Fishman S, SA Gardiner, Guarneri I 2006 Phys. Rev. Lett. 96 164101
[34] ］Fang J Q, Li Y 2009 First International Conference, Complex 2009 (Berlin：Springer) p1678
[35] ］Li Y, Fang J Q, Liu Q 2009 Journal of Systems Science and Complexity (to be published)
[36] ］Liu Q, Fang J Q, Li Y Acta Phys.Sin. (in Chinese)(in Press) (Accepted)［刘强、方锦清、李永 (已接受)］
[37] ］Liu F, Cao P J, Zhang H R, Tian J F, Xiao C W, Shen C M, Li J Q, Gao H J 2005 Advanced materials 17 1893
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