Research And Application Of The Scale-free Network Model

In the past few years,scale-free property has been discovered from many real-world networks such as www networks,Internet networks,collaboration networks,wealth distribution networks,metabolic network and so on,which has been attracting researchers'attention on the complex network as relevant to many fields of science.However,due to the large size and complex structure,we know less about the topological structure,hierarchical organization and evolving process based on the real-life network.This thesis,combines the statistical properties of the real network, theoretical analysis with computer simulation,and does some researches on the topological structure.The evolving mechanism of BA model is investigated at length, and four scale-free network models,which is closer to the real-life network,are proposed from a different angle.The research work in this paper helps to know more about the scale-free network,and provides theoretical basis and practical direction for designing new network with the good performance.The main research work is as follows:(1) An extended BA model is presented.Growth and preferential attachment is two indispensable conditions developed the power-law distribution,which is the core of the BA model.In fact,the connection of the different nodes in many real networks is random.Based on BA model,a probability parameter p controlling the network's topology is introduced,and a hybrid links BA model is conceived.Theory analysis and simulation result show that extended BA model'topology structure are closer to the real-life network than BA model,and its distribution with non-power property is between exponential and power function.At last,the application in the social economics is discussed. (2) Base the iteration,two hierarchical models are proposed.In order to describe the real-life networks with high clustering scale-free property,a new iterative mechanism is imported,and the two hierarchical network model from the easy to the difficult and complicated are conceived.First of all,a hierarchical network model based on the edge iteration is investigated,and then a edge are extended into a module of d-clique,a hierarchical network model based on apollonian filling is investigated. The theoretical analysis and the computer simulation show that the model contains high clustering property and scale-free property.At last,the application in the economic management is discussed and analyzed,shows theoretical guidance and realistic meaning.