A New Type Of Planar Network With High Clustering And High Entropy

Small-world networks are ubiquitous in real-life systems, such as the WorldWide Web, communication networks, and electric power grids, and most of them arestochastic. The randomness, while conforms to the characteristics of real system, butit is difficult to make people to get a intuitive understanding of how networks areformed, as well as how the interaction between different nodes in the network. Whilethe deterministic models for complex networks play all indispensable role in the fieldof network modeling. In this paper, we present a model that generates a small-worldnetwork in a simple deterministic way and analyze the relevant topological propertiesof the model, such as the degree distribution, clustering coefficient, and diameter.Meanwhile, according to the special structure of the model, we derive analytically theexact numbers of spanning trees in the planar networks. The results show that themodel has a discrete exponential degree distribution, high clustering coefficient, shortdiameter, and high entropy.In chapter1, we mainly presentation the background, the meaning and thesituation of the complex network and deterministic model.In chapter2, some of the concepts, definitions and lemmas involved. At thesame time, some formulas, which used to calculate the number of spanning trees, arelisted.In chapter3, we introduce a deterministic small-world networks model,according to its special structure, we analyze the relevant topological properties andthe number of spanning trees of the modelIn the last chapter, this artical is summarized, and some problems are discussedby us.