Approximating the Spectrum of a Graph

The spectrum of a network or graph G=(V,E)with adjacency matrix A , consists of the eigenvalues of the normalized Laplacian L= I - D^-1/2 A D^-1/2 This set of eigenvalues encapsulates many aspects of the structure of the graph, including the extent to which the graph posses community structures at multiple scales. We study the problem of approximating the spectrum, łambda = (łambda_1,\dots,łambda_|V| ) of G in the regime where the...