Abstract:

We investigated the convergence of the empirical spectral distribution (ESD) of normalized Laplacian matrix from random graph with given expected degree. It was shown that the ESD of normalized Laplacian matrix converges to a fixed probability distribution when the expected degree satisfys some assumptions, but the fixed probability distribution may be different at different places.

Key words:  random graph, random matrix, normalized Laplacian matrix, empirical spectral distribution