Analysis of Internet Topologies

The discovery of power-laws and spectral properties of the Internet topology illustrates a complex underlying network infrastructure that carries a variety of the Internet applications. Analysis of spectral properties of the Internet topology is based on matrices of graphs capturing Internet structure on the Autonomous System (AS) level. The analysis of data collected from the Route Views and RIPE projects confirms the existence of power-laws and certain historical trends in the development of the Internet topology. While values of various power-laws exponents have not substantially changed over the recent years, spectral analysis of matrices associated with the Internet graphs reveals notable changes in the clustering of AS nodes and their connectivity. It also reveals new historical trends in the clustering of AS nodes and their connectivity. These properties of the Internet topology may be further analyzed by examining element values of the corresponding eigenvectors.