Spectral analysis of Internet topologies

Spectral analysis of the Internet topology at the autonomous system (AS) level is performed by adapting the standard spectral filtering method of examining the eigenvectors corresponding to the largest eigenvalues of matrices related to the adjacency matrix of the topology to suggest clusters of ASs with natural semantic proximity.

Abstract

Spectral analysis of the Internet topology at the autonomous system (AS) level, by adapting the standard spectral filtering method of examining the eigenvectors corresponding to the largest eigenvalues of matrices related to the adjacency matrix of the topology is performed. We observe that the method suggests clusters of ASs with natural semantic proximity, such as geography or business interests. We examine how these clustering properties vary in the core and in the edge of the network, as well as across geographic areas, over time, and between real and synthetic data. We observe that these clustering properties may be suggestive of traffic patterns and thus have direct impact on the link stress of the network. Finally, we use the weights of the eigenvector corresponding to the first eigenvalue to obtain an alternative hierarchical ranking of the ASs.