Study on the stability of the topology interactive growth mechanism using graph spectra

In terms of spectral graph theory, the graph spectrums represent more accurate structural properties and robust characteristics of the network topologies. In this study, the authors study the stability characteristics of the normalised Laplacian spectrum associated with the interactive growth mechanism for the increasing of nodes in the generation of large-scale autonomous systems (AS) graphs. With consecutive snapshots of the AS-level Internet topologies, the authors obtain the stable models of the spectrum. In addition, the authors investigate the stability conditions of the spectrum based on the interactive growth mechanism and the comparisons with other metrics and study how to influence the spectrum by the inputs of the interactive growth mechanism.