基于Sierpinski分形垫的确定性复杂网络演化模型研究

近年来,人们发现大量真实网络都表现出小世界和无尺度的特性,由此复杂网络演化模型成为学术界研究的热点问题.本文基于Sierpinski分形垫,通过迭代的方式构造了两个确定性增长的复杂网络模型,即小世界网络模型(S-DSWN)和无尺度网络模型(S-DSFN);其次,给出了确定性网络模型的迭代生成算法,解析计算了其主要拓扑特性,结果表明两个网络模型在度分布、集聚系数和网络直径等结构特性方面与许多现实网络相符合;最后,提出了一个确定性的统一模型(S-DUM),将S-DSWN与S-DSFN纳入到一个框架之下,为复杂网络的相关研究提供理论基础.特别地,发现这些网络模型都是极大平面图.

Research on the deterministic complex network model based on the Sierpinski network

In the last few years, the complex network has received considerable attention. It is proven that the small-word effect and scale-free property exist in various real-life networks. In this paper, based on the deterministic fractal-the Sierpinski gasket, two deterministic complex network evolving models, S-DSWN and S-DSFN, are proposed by iterative approach. S-DSWN can generate small-world network, while S-DSFN can generate scale-free networks. The iterative algorithms to generate the models are also designed. Then, some relevant characteristics of the networks, such as degree distribution, clustering coefficient, and diameter, are computed or predicted analytically, which match well with the characterizations of various real-life networks. Finally, an integrated model is introduced to unify S-DSWN and S-DSFN into the same framework, which makes it convenient to study the complexity of the real networked systems within the framework of complex network theory. Moreover, we have proven that these network models are maximal planar graphs.