﻿ 一类确定性小世界网络模型及特性分析

# 一类确定性小世界网络模型及特性分析A Kind of Deterministic Small-World Networks Model and Analysis of Their Characteristics

Abstract:
Deterministic small-world network is an important branch of study of complex networks. In 2008, Zhang et al. in Eur.Phys.J.B 63 have offered detailed topological characteristics of the deterministic uniform recursive tree from the viewpoint of complex network. They derived topological characteristics of the deterministic uniform recursive tree. It shows a logarithmic scaling with the size of the network; however its clustering coefficient is zero. In 2012, Lu et al. in Physica A 391, based on the deterministic uniform recursive tree and by a simple rule, added some edges and got a deterministic small-world network model. In this paper, we study the law of the structure on the basis of the model constructed in Physica A 391 from a new viewpoint, naturally, we generalize and change the rule to get an iterated class of small-world networks, and then give the analytic solutions to several important topological characteristics of these models proposed. The obtained vigorous results show that these networks have power-law cumulative degree distribution, high clustering coefficient and small diameter.

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