The Study on Fractals of Internet Router-level Topology

The analysis on the degree distribution and spectral density of graph spectrum of Internet topology structure is the principle content of modeling on Internet router-level topology. In this paper, we studied the fractal features of Internet topology structure. According to the sample algorithm, we got two different groups of sample topologies from Internet topology measuring data of CAIDA. We analyzed the degree distribution in each sample topology and found that they satisfied power law. This is coincident with the degree distribution of the whole Internet topology. Then, we analyzed the distribution of the spectral density of the Internet sample topologies. By analyzing the distribution of spectral density with eigenvalues of each sample topology, we found that the results of them showed highly coherence. At last, we analyzed signless Laplacian spectra(SLS) on three sample topologies with 3000 nodes showed that SLS distribution results were very much similar with each other though the sample topologies were quite different. All of these prove that there exist self-similarity among the parts of Internet topology structure and between the part and the whole of Internet topology. So we can conclude that Internet topology structure has got fractals.