On Laplacian and normalized Laplacian of a social network

Abstract

In the task of structural identification of a network a vital tool is the underlying spectrum associated with the normalized graph Laplacian. To comprehend such spectrum, we need to determine the eigenvalues. In this paper we have found certain useful bounds involving the eigenvalues of both combinatorial Laplacian and normalized Laplacian and applied the same on a collaboration graph obtained from a social network.