Generalized Farey Tree Network with Small-World

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.