Application of normalized Laplacian spectra for multicast routing evaluations

The multiplicity of the eigenvalue 1 (ME1) and the weighted spectral distribution (WSD), i.e., two weakly-related metrics defined on the normalized Laplacian spectrum, capture the size-independent features of the Internet structure. In this paper, we evaluate the multicast routing protocol in the size-independent Internet structure, and numerically find that the protocol indexes tend to stable as the network size increases if the normalized Laplacian spectrum of the network topology is asymptotically independent of the network size. The real-world Internet topology evolves (i.e., the network size increases) over time, which indicates that the protocol should be evaluated in the size-independent network structure. Our studies provide a specific application of the normalized Laplacian spectrum, which verifies that the size-independent structure captured by the spectrum is useful for the evaluation of network protocols.