Performance of Two Normalized Laplacian Spectral Features on Sampling Algorithms

Our recent studies confirmed that two normalized Laplacian spectral features, namely the multiplicity of the eigenvalue 1 (ME1) and the weighted spectral distribution (WSD), are critical for the robustness of the size-independent Internet structure. In this paper, we evaluate the two spectral features based on the comparison between real-world evolving Internet data and a sequence of sampling graphs acquired by an original Internet topology. The numerical analysis of the comparison verifies that biased sampling algorithms should be paid more attention for the Internet structure, because the two spectral features perform much better on biased sampling graphs compared to those on unbiased sampling graphs.