A New Class of the Planar Networks with High Clustering and High Entropy

Abstract

Small-world networks are ubiquitous in real-life systems, such as the World Wide Web, communication networks, and electric power grids, and most of them are stochastic. In this paper, we present a model that generates a small-world network in a simple deterministic way and analyze the relevant topological properties of the model, such as the degree distribution, clustering coefficient, and diameter. Meanwhile, according to the special structure of the model, we derive analytically the exact numbers of spanning trees in the planar networks. The results show that the model has a discrete exponential degree distribution, high clustering coefficient, short diameter, and high entropy.