Fractal Statistic on the Self-similarity of Internet Router-level Topology

Because the statistical method with multi-angle and multi-measurement has many problems,a method to depict the overall Internet topology characteristics by using network fractal dimension was proposed in the paper.With the basement of the traditional fractal theory,combined with the self-similarity of Internet topology,the related concepts of the network topology dimension were given.By the mapping from Euclidean space to topology structure,the network topology dimension had been analyzed deeply and then the definitions of weighted network topology dimension and the computation method were given.By computing some main measurements in Internet topology such as power-law distribution and clustering,we analyzed the relationship between the network topology dimension and the traditional statistical method,described the advantage to depict network integral properties using network topology dimension.