随机图、层次结构和节点度，是AS级Internet网络拓扑仿真的常用模型。然而，这些模型是相应网络结构的简化描述，导致仿真拓扑图在局部连通性等尺度上表现出不精确性。根据谱图理论，正规Laplacian图谱能够更精确地建模相应AS图结构的全局节点分类和局部连通性特征。因此，本项目深入挖掘正规Laplacian图谱在不同节点规模拓扑图演化过程中的稳定不变特征，并针对Internet测试床难以紧跟真实Internet爆炸式节点规模增长趋势的现实问题，从图谱演化建模、交互增长与节点偏好连接模型优化、图扰动与图谱变化关联挖掘、逼真度综合评估等方面，开展基于正规Laplacian图谱的AS级Internet网络拓扑建模、仿真与评估方法的研究。研究成果，对于限定节点规模条件下的Internet测试床拓扑结构仿真及其逼真度综合评估，以及Internet技术开发、测试与评估方法的研究等，具有重要意义。

Random graph, hierarchy structure and nodes degree are the typical models for the simulation of the AS-level Internet topology. However, those models are the simple descriptions of the corresponding network structure, which induces the inaccuracy of the synthetic graphs on the metrics associated with local connectivity. With spectral graph theory, the normalized Laplacian spectrum (nls) is a more accurate model for the corresponding AS graphs and can be used to capture the characteristics of global nodes classification and local connectivity. Therefore, this program mines the stable properties of the nls with the Internet evolving. In addition, for the problem that it is difficult for the Internet test bed to match the scale of the real Internet with explosive growth of nodes, this program studies the modeling, simulation and evaluation methods for the AS-level Internet topology based on the nls, e.g. modeling the evolvement characteristics of the nls, optimizing the interactive growth mechanism and nodes preferential attachment models, mining the relationships between graph perturbation and corresponding changes in the nls, evaluating the fidelity of the synthetic AS graph with different topology metrics, etc. The results of this program will be significant for the topology simulation and corresponding fidelity evaluation of the Internet test bed with limit scale and the research for the development, test and evaluation methods of the Internet technology.