Generalized Farey Tree Network with Small-World

  • Jin-Qing Fang
  • Yong Li
Part of the Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering book series (LNICST, volume 5)


Generalized Farey tree network (GFTN) model with small-world is proposed, and the topological characteristics are studied by both theoretical analysis and numerical simulations, which are in good accordance with each other. Analytical results show that the degree distribution of the GFTN is exponential. As the number of network nodes increasing with time interval (or level number), t, the clustering coefficient of the networks tends to a constant, ln2; the diameter of the network is increasing with t, the resulting networks are evolved from disassortative to assortative and show assortative coefficient tends to 0.25 for large t.


Generalized Farey tree network topological properties theoretical analysis small world numerical simulation 


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  1. 1.
    Kim, S.H., Ostlund, S.: Simultaneous rational approximations in the study of dynamical systems. Phys. Rev. A. 34, 3426–3434 (1986)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Maselko, J., Swinney, H.L.: A Farey triangle in the Belousov-Zhabotinskii reaction. Phys. Lett. A. 119, 403–406 (1987)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Fang, J.Q.: Generalized farey organization and generalized winding number in a 2-D DDDS. Phys. Lett. A. 146, 35–44 (1990)CrossRefGoogle Scholar
  4. 4.
    Calvo, O., Cartwright, J.H.E., Gonzalez, D.L., et al.: Three-frequency resonances in coupled phase-locked loops. IEEE Transactions, Circuits and Systems I: Fundamental Theory and Applications 47(4), 491–497 (2000)CrossRefGoogle Scholar
  5. 5.
    Fang, J.Q., Wang, X.F., Zheng, Z.G., et al.: New interdisciplinary science: network science(I) (in Chinese). Prog. In Phys. 27(3), 239–343 (2007)Google Scholar
  6. 6.
    Fang, J.Q., Wang, X.F., Zheng, Z.G., et al.: New interdisciplinary science: network science(II) (in Chinese). Prog. In Phys. 27(4), 361–548 (2007)Google Scholar
  7. 7.
    Newman, M.E.J.: Assortative Mixing in Networks. Phys. Rev. Lett. 89, 208701 (2002)CrossRefGoogle Scholar
  8. 8.
    Fang, J.Q.: Briefly review on complex network pyramid and their universality-complexity. In: Fang, J.Q. (ed.) Proceedings of CCAST(WL) Workshop Series: Forth National Forum on Network Science and Graduate Student Summer School, vol. 191, pp. 204–221. CCAST, Beijing (2008)Google Scholar

Copyright information

© ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering 2009

Authors and Affiliations

  • Jin-Qing Fang
    • 1
  • Yong Li
    • 1
  1. 1.China Institute of Atomic EnergyBeijingChina

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