Spectral analysis of Internet topology graphs

The discovery of power-laws and spectral properties of the Internet topology indicates a complex underlying network infrastructure. Analysis of spectral properties of the Internet topology has been usually based on the normalized Laplacian matrix of graphs capturing Internet structure on the Autonomous System (AS) level. In this paper, we first extend the previous analysis of the Route Views data to include datasets collected from the RIPE project. Spectral analysis of collected data from the RIPE datasets confirms the previously observed existence of power-laws and similar historical trends in the development of the Internet. Presented spectral analysis of both the adjacency matrix and the normalized Laplacian matrix of the associated graphs also reveals new historical trends in the clustering of AS nodes and their connectivity. The connectivity and clustering properties of the Internet topology are further analyzed by examining element values of the corresponding eigenvectors.