| The modeling of evolutionary networks is an important part of complex networks research.Studying the evolution mechanism of networks can effectively help people understand properties driving the evolution of real-world networks,which plays an important role in the study of network dynamics.The rapid development of the Internet has brought tremendous changes to the way of human life,so it is very important to study the modeling and evolution of the Internet.Autonomous system(AS)network is an important part of the Internet,so this thesis focuses on the modeling and evolution of AS IPv6 network,which has an important application in providing AS-level Internet topology generators.In addition,geometry is an important method to study problems.Identifying the hidden geometric structures behind complex networks can effectively help people understand the formation mechanism of networks.In the study of complex networks,the classical geometric assumption is European space.However,many real networks show hyperbolic characteristics in the evolution process.Therefore,this paper will study the evolution characteristics of AS IPv6 networks based on hyperbolic space assumption and network topology.The research of this thesis mainly includes the following three aspects:1.Based on the complex networks theory,the network topology and evolution characteristics are analyzed from the aspects of network scale,network sparsity and clustering characteristics.The results indicate that AS IPv6 evolves linearly with time,and the network becomes more closely,shows stable heterogeneity and clustering characteristics.In addition,the "popularity-similarity" maximization model is used to simulate the real-world network to provide the necessary parameters for embedding the real network into hyperbolic space,and our experiments verify the reliability of the simulation network.Finally,the real network is embedded in hyperbolic space by hybrid model combining the model based on neighbor nodes and the model based on common neighbor nodes,and the hyperbolic evolution characteristics of AS IPv6 network are quantitatively analyzed.It is found that the evolution of AS IPv6 network presents hierarchical characteristics.The evolution of AS IPv6 network is diversely analyzed from the perspective of topological structure and hyperbolic space.2、The evolution of AS IPv6 network is studied by combining the characteristics of topological structure with hyperbolic space,and the relationship between the characteristics of topological structure and hyperbolic space is analyzed.Firstly,the relationship between hierarchical index and topological structure in a single network is investigated.The results show that the hierarchical index of a node is negatively correlated with the degree,k-core as well as the betweeness of the node.Secondly,using different topological characteristics to classify nodes in the network,this thesis studies the evolution of average angular distance,average hyperbolic distance and average connection probability between different kinds of nodes,and further investigated the strength of similarity links,the influence of popularity links and similarity links.We show the evolution characteristics tend to establish links under different partitions in the evolution of AS IPv6 networks.The results show that the evolution of hyperbolic characteristics among nodes under different classifications has a relatively stable interval distribution.From the perspective of hyperbolic space,this thesis deeply studies mechanisms of network establishment and evolution which can provide a theoretical basis for promoting the better development of the Internet.3 、 The generation methods of AS IPv6 backbone network are proposed.By comparing and analyzing the differences between the backbone network and the original network in the topological structure and hyperbolic spatial characteristics,two methods of backbone network generation algorithms,the observation filtering method based on the principle of "repulsion-attraction" weighted and the backbone network method based on community partition,are used to represent the original network,including.Through the backbone network,we can model the AS IPv6 based on hyperbolic space assumption which can effectively reduce the time cost of network evolution research in hyperbolic space. |
