摘要
针对路由级Internet宏拓扑结构进行了谱密度分布分析与无符号拉普拉斯谱(SLS)分布分析。首先通过对拓扑结构各异的5种采样拓扑图,分别进行谱密度-特征值分布分析,发现5组分析结果表现出高度的一致性,证明了Internet拓扑结构的自相似性,也证明了采样拓扑可以再现局部Internet拓扑结构特征。然后通过采样拓扑图的谱密度-特征值分布函数与ER图、BA无尺度网络拓扑图进行比较,发现三者具有明显区别,得出谱密度-特征值分布函数可作为分辨图谱拓扑结构有效方法的结论。最后通过4组3000点采样拓扑进行SLS分布分析,发现尽管4组3000点采样路由与连接互不相同,但SLS谱分布却非常相似,4组采样拓扑在特征值λ=1处重数均较高,重数次高的特征值都群聚在λ=2处。在特征值从2～103变化过程中表现出较明显的幂律分布特性,其幂指数值保持在3.2813至3.8013之间,特征指数接近。该结论为Internet宏观拓扑结构建模研究提供了量化判据,是Internet拓扑建模研究的重要内容。
Analysis of spectrum density and SLS（signless Laplacian spectra） on router-level macroscopic toplogy was performed. Firstly, we found in experiments that five analysis results of spectrum density on five sampling topologies showed highly similarity proving that Internet is a system of self-similarity as well as the ability for sampling topology to resemble the whole Internet topology. Secondly, obvious difference between the spectrum density analysis results of sampling topology, ER graph and BA graph indicated that spectrum density analysis is a good way to distinguish graphs. Finally,analysis of SLS on four groups of sampling topology with 3000 nodes showed that SLS distribution re- sults were very much similar with each other though the topology samples were quite different. All four analysis results had high tuples at λ=1 and second high tuples at λ=2. Besides, principle of the power law distribution was observed from SLS analysis when eigenvalue in SLS ranged from 2 to 103, proving in another aspect that Internet topology had property of self-similarity. The research results above could be regarded as quantitative judgements during the research of modeling on Internet macroscopic topology.
出处
《计算机科学》
CSCD
北大核心
2008年第12期34-38,共5页
Computer Science
基金
国家高技术研究发展计划(2001AA415320)
