Spectrum Density Analysis on Router-level Internet Macroscopic Topology

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 results 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.