On The Research Of Two Kinds Of Deterministic Small World Networks

The deterministic model of complex networks plays an important role in the modeling field of complex networks. It can reflect the real system. Through the research of the related parameters of the network, we can clearly understand the topology of the networks and comprehensively grasp the local and global characteristics of the networks. In this paper, using the method of iteration and line graph operations, we mainly study the formation mechanism of the deterministic small world network and analyze the topological properties of the constructed network.This paper mainly research two kinds of problems as follows:Firstly, we have presented a deterministic small-world model derived from the star-binary tree. By adding links between each pair of full-brother nodes, and adding links between the grandfather node and its grandson nodes, we get a small-world network with high clustering coefficient not less than 0.7333. We obtain the analytic solution for degree distribution, clustering coefficient, clustering-degree correlation and diameter of the deterministic model. We also give a new way to generate a network with specific properties by modifying an existing network.Secondly, we preliminary discussed the relationship between the line graph of a tree with small world network and the tree. Then we focus on a method for constructing new deterministic small-world network by the line graph operation in each deterministic uniform recursive tree. The line graph operation brings about cliques at each node of the previous given graph, and the resulting line graph possess larger clustering coefficients. Deterministic networks can analyze the network characteristics, and the results can be used to indirectly test the correctness of the stochastic model and method.