On Construction,Properties And Community Structure Of Several Scale-free Network Models

The research of complex network is an important topic of network research,its complexity manifests itself in the following aspects:the complexity of the topology of the network itself;the growth mechanism of the internet is complex,because the growth process is accompanied by the addition and disappearance of vertex and edge;the pattern of connect between vertices is diverse,and the edges of some networks in life still have direction;kinetic complexity and so on,these complexities can exist at the same time,and these complexities bring difficulties to the research process of the network.Complex network technology can intuitively show the various elements of the complex network system associated interaction,and it can also deeply analyze the structure characteristics and rules of complex system,therefore,it is widely used in various fields of life.Scale-free network is an important branch in complex networks,a majority of studies show that the vast majority of real networks are scale-free net-works,such as the World Wide Web,social network,metabolic network and so on are closely related to us.In order to better depict and understand the topological structure and related properties of scale-free network,network model is often chosen to simulate real networks.Researchers have proposed many network model,but mostly is certain and spe-cial model.In fact the network is random and have extremely complex dynamic structure,rather than regular,the way of growth not show very strong regularity,so this article defines several network operations and several kinds of dynamic scale-free network models are constructed from the perspective of network model topology and network operation,including SA-mixed network model,AS-mixed network model,hy-pernetwork model and generalized compound network model,these models are more random and the generation mechanisms of these models are different,the topology of these models is analyzed in this article by analyzing the spectrum and calculating the average degree,the degree accumulation and other parameters.The growth rate of the network model is estimated by the new definition called velocity,the paper also describes its scale-free property from the perspective of concept and differential equation.