Graph sampling for Internet topologies using normalized Laplacian spectral features

Abstract

A crucial task in the process of constructing Internet testbeds is to substantially reduce the number of nodes in the interdomain Internet topology, while maintaining its essential properties. In this paper, we first decompose the Internet topology into seven bipartite graphs, a matching graph and a core graph using two normalized Laplacian spectral features, namely, the weighted spectral distribution and the multiplicity of the eigenvalue 1. Then, we accomplish a marked reduction in size of the topology by sampling and merging these graphs. The proposed approach was tested on realistic Internet graphs that were explored from 2000 to 2016 and a large-scale simulated graph. The experimental results confirm that our approach can effectively reduce the number of nodes in these graphs by more than 96%, while maintaining their essential properties.