Research On The Characteristics And Evolution Behavior Of Scale-free Networks

At the beginning of the 21st century,the sciences of complexity and their complexity research attracts more and more attention at home or aboard,scale-free network research is an important part of the sciences of complexity research.The results show that the brain structures from the organism to various metabolic networks,from the Internet to the WWW,from large-scale power networks to the global transportation networks,which all have small-world phenomena or the scale-free character of the complex network in the real world.Study of complex networks has attracted wide attention from different disciplines,has become a challenging research topics.In the field of educational technology studies,a growing number of learners using online education,distance education to learn and acquisitive resource,and the networks that learners use have become a huge complex network,which consists of the mutual links learners and resources.We build a topology network to study education network,to explore the learning methods and ways of resource acquisition.The paper mainly focus on scale-free network theory and application,researching include the characteristics of scale-free networks,the nature of the model evolution,as well as the reality network,the mainly contents include power-law distribution,changes of topological features and scale-free characteristics of education network.The major contributions of this paper are:1.Construction of evolution model.Scale-free network as a special kind of network topology in complex network,which own characteristics related to many factors,therefore,the paper based on the underlying network model to construct different character models.By introducing the direction we build scale-free network model with directions;and introducing weights to build scale-free network,according to those generated by scale-free networks,we can explore the analysis of the nodes distribution,the average shortest path length.2.Empirical study and analysis education network.According scale-free network theory and model,the paper applies the scale-free network theory and method to real network research.We chose the education resources network in the field of education technology,through collecting dates that webpage's hyperlinks among education resources network to construct a topology network of hyperlinks.By anglicizing the topology network,we find education resource network is a scale-free network,and the nodes distribution follows power-law distribution,then we statistic other topology features,include the shortest path network distribution,power-law distribution,modularity.3.Build the simple network topology platform.Complex network contain a large number of network models,scale-free model is the one of them.Through statistical models and classification,then use the existing algorithms to construct simple network topology platform,through network topology platform that can generate typical complex network models,such as the small-world networks,random network,complete graphs,etc.,while the definition of the topological characteristics of the statistical functions.