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构建了三类确定性加权广义Farey组织的网络金字塔.理论推导并数值计算了网络金字塔的拓扑性质（度分布、平均最短路径、平均聚类系数和相称性系数等）, 进而将Farey序列作为网络节点的确定、随机和混合的三种权重值，以此为基础计算并拟合了三类网络金字塔的点的强度分布和边的权重分布.计算结果初步揭示了加权广义Farey组织的网络金字塔的复杂性特征，有助于了解一些实际网络的复杂性和多样性.
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关键词:
- 广义Farey组织的网络金字塔 /
- 金字塔结构 /
- 混合连接
Three types of deterministic weighted generalized Farey organized network pyramids(so-called WGFONP-1,WGFONP-2, WGFONP-3) are constructed, and the topological characteristics (degree distribution, average path length, clustering coefficient, assortative coefficient and so on) of network pyramids are studied by theoretical and numerical analyses. Using Farey sequence as determinacy, randomicity and hybrid weights of network nodes, we calculate and fit the strength distribution and the weight distribution of the network pyramids, as well as tentatively reveal the complexities and the diversities of the WGFONP-1,WGFONP-2 and WGFONP-3. These results can conduce to the understanding of complexities and diversities of a number of practical networks.[1] ［1］ Watts D J, Strogatz S H 1998 Nature 393 440
[2] ［2］ Baraba′si A L, Albert R 1999 Science 286 509
[3] ［3］ Oltvai Z N, Baraba′si A L 2002 Science 298 763
[4] ［4］ Fang J Q, Li Y, Bi Q 2007 Int. J. Mod. Phys. B 21 5121
[5] ［5］ Fang J Q, Bi Q, Li Y, Lu X B, Liu Q 2007 Sci. China G 50 379
[6] ［6］ Fang J Q, Bi Q, Li Y, Lu X B, Liu Q 2007 Adv. Comp. Syst. 10 117
[7] ［7］ Fang J Q, Li Y 2008 Adv. Mech. 38 663 (in Chinese)［方锦清、李永 2008 力学进展 38 663］
[8] ［8］ Fang J Q 2009 Int. J. Syst. Con. Commun. 1 453
[9] ［9］ Fang J Q 2007 Prog. Nat. Sci. 17 361
[10] ］ Fang J Q, Bi Q, Li Y, Lu X B, Liu Q 2007 Chin. Phys. Lett. 24 279
[11] ］ Li Y, Fang J Q 2009 The First International Conference on Complex Systems: Theory and Applications (Part Ⅱ) (Berlin: Springer-Verlag) p1238
[12] ］ Fang J Q, Li Y 2009 The First International Conference on Complex Systems: Theory and Applications (Part Ⅰ) (Berlin: 2 Springer-Verlag) p78
[13] ］ Fang J Q 1990 Phys. Lett. A 146 35
[14] ］ Calvo O, Cartwright J H E, Gonzalez D L, Piro O, Sportolari F 2000 IEEE Trans. Circ. Syst. 47 491
[15] ］ Kim S H, Ostlund S 1986 Phys. Rev. A 34 3426
[16] ］ Maselko J, Swinney H L 1987 Phys. Lett. A 119 403
[17] ］ Zhou L, Gong Z Q, Zhi R, Feng G L 2008 Acta Phys. Sin. 57 7380 (in Chinese) ［周磊、龚志强、支蓉、封国林 2008 物理学报 57 7380］
[18] ］ 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 物理学报 55 4051］
[19] ］Liang S M 1996 Chinese：Social Life (Beijing：China Federation of Literary and Art Circles Publishing Corporation) p1 (in Chinese) ［梁漱溟 1996 中国人: 社会人生（北京：中国文联出版社） 第1页］
[20] ］ Wang X Q, Wu S F, Jiang G S, Pan S 2003 Phys. Lett. A 319 514
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[1] ［1］ Watts D J, Strogatz S H 1998 Nature 393 440
[2] ［2］ Baraba′si A L, Albert R 1999 Science 286 509
[3] ［3］ Oltvai Z N, Baraba′si A L 2002 Science 298 763
[4] ［4］ Fang J Q, Li Y, Bi Q 2007 Int. J. Mod. Phys. B 21 5121
[5] ［5］ Fang J Q, Bi Q, Li Y, Lu X B, Liu Q 2007 Sci. China G 50 379
[6] ［6］ Fang J Q, Bi Q, Li Y, Lu X B, Liu Q 2007 Adv. Comp. Syst. 10 117
[7] ［7］ Fang J Q, Li Y 2008 Adv. Mech. 38 663 (in Chinese)［方锦清、李永 2008 力学进展 38 663］
[8] ［8］ Fang J Q 2009 Int. J. Syst. Con. Commun. 1 453
[9] ［9］ Fang J Q 2007 Prog. Nat. Sci. 17 361
[10] ］ Fang J Q, Bi Q, Li Y, Lu X B, Liu Q 2007 Chin. Phys. Lett. 24 279
[11] ］ Li Y, Fang J Q 2009 The First International Conference on Complex Systems: Theory and Applications (Part Ⅱ) (Berlin: Springer-Verlag) p1238
[12] ］ Fang J Q, Li Y 2009 The First International Conference on Complex Systems: Theory and Applications (Part Ⅰ) (Berlin: 2 Springer-Verlag) p78
[13] ］ Fang J Q 1990 Phys. Lett. A 146 35
[14] ］ Calvo O, Cartwright J H E, Gonzalez D L, Piro O, Sportolari F 2000 IEEE Trans. Circ. Syst. 47 491
[15] ］ Kim S H, Ostlund S 1986 Phys. Rev. A 34 3426
[16] ］ Maselko J, Swinney H L 1987 Phys. Lett. A 119 403
[17] ］ Zhou L, Gong Z Q, Zhi R, Feng G L 2008 Acta Phys. Sin. 57 7380 (in Chinese) ［周磊、龚志强、支蓉、封国林 2008 物理学报 57 7380］
[18] ］ 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 物理学报 55 4051］
[19] ］Liang S M 1996 Chinese：Social Life (Beijing：China Federation of Literary and Art Circles Publishing Corporation) p1 (in Chinese) ［梁漱溟 1996 中国人: 社会人生（北京：中国文联出版社） 第1页］
[20] ］ Wang X Q, Wu S F, Jiang G S, Pan S 2003 Phys. Lett. A 319 514
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