Research On Deterministic Models For Complex Networks And Its Applications

Complex Systems are widely present in nature and human society. Complex Networks can be used suitably to describe Complex Systems. In recent decades, scholars have done a lot of studies for complex networks from multi-angle and multi-field, such as the theoretical models, the empirical studies of the real-world networks, and the application of the theories of network sciences. The network modeling is an active research field, which has been studied in the early researches and achieved many results nowadays, among that of complex networks. Constructing the network models in a deterministic fashion is not only of the important theoretical significance, but also of the practical application values.In this paper, we mainly study two aspects, complex network modeling, and the LDPC codes in the framework of complex network theories. We propose two deterministic network models, and analyze their basically topological characteristics; moreover, a configuration scheme of LDPC code is given by applying the theories of complex networks.The main works in this paper are as follows:(1) Based on one of the famous regular fractals, Durer pentagon, we construct a deterministic network, called Durer network, by a mapping method, and analyze its topological characteristics concisely, which show that Durer network contains some principal features in most real network systems. Its degree distribution satisfies the power-law distribution with the power exponent2to3, furthermore, it has a high clustering coefficient and short path length, showing that Durer network is a scale-free and small-world network.(2) We generate a deterministic hierarchical network by mapping the recursive graph of a polygon, and analyze its topological characteristics, including degree distribution, the clustering coefficient, the network diameter, average path length, and degree correlations. We obtain that this network is not a scale-free network, but a small-world network. Hereafter, we propose a method that makes this hierarchical network scale-free.(3) We analyze the relationship between the decoding performance of LDPC code and the distance between variable nodes on the basis of the theories of complex networks. Taking into account that scale-free networks have a short average path, we propose a method to design LDPC code from the perspective of scale-free network models, which provides a new perspective for the study of LDPC code.