On Model Constructions And Method Connections To Scale-free Networks

Complex network is a hot topic in today's research,especially for the scale-free network research.Scale-free networks are randomly changing over time.This chang-ing phenomenon has brought great difficulties to study of scale-free networks.In addition,because dynamic phenomena of real networks have rich micro-structures and corresponding complex dynamics,their structure and nature are unable to use the local information to carry on the forecast.However,for the study of complex net-works,it is necessary to master the topological structures of scale-free networks.In this paper,we present some new methods for the analysis of complex networks,struc-ture is very necessary.The domestic and foreign scholars are devoted to researching and constructing a series of scale-free properties of networks in order to approximate estimates of the real networks.The establishment of a scale-free network model is an important way to approx-imate a real network with a special network.It is worth that the scale-free network model has a good structure just for the practical application of the structure of the model to provide a reliable theoretical support.In this paper,we first give out some specific mechanisms of growing network models,and then proceed from the degree spectrum,cumulative degree distribution of several aspects of analysis and discussion of nature of scale-free networks.Based on the existing statistical methods:such as cumulative distribution,clustering distribution and average path length,we provide new statistical ways:edge cumulative distribution and three kinds of edge-vertex cumulative distribution.The maximum leaf spanning trees of growing networks are given by algorithms.In addition,the growing rate and the degree distribution of net-works are used to compare the advantages and disadvantages of two network models,and the indexes of evaluation network models are listed.Inspired by the operation of graphs in graph theory,we give some concrete ways of making graphs of the minimum dominating set of two scale-free networks,such as join product and cartesian product.Then,some criteria for measuring the quality of a scale-free network are listed.At the end of this paper,we summarize,provide our problems or conjectures and forecast the future researching work.