Title:  Network Analysis with Matrix Functions

Abstract:  Networks arise in many applications. It is often of interest to be able to identify the most important nodes of a network or to determine the ease of traveling between them. We are interested in carrying out these tasks for large undirected and directed networks.  Many quantities of interest can be determined by computing certain matrix functionals.  We discuss how for directed and undirected graphs a few steps of the Lanczos method in combination with Gauss-type quadrature rules can be applied to determine upper and lower bounds for quantities of interest.