Spectral bounds for the betweenness of a graph

In this paper we find spectral bounds (Laplacian matrix) for the vertex and the edge betweenness of a graph. We also relate the edge betweenness with the isoperimetric number and the edge forwarding and edge expansion indices of the graph allowing a new upper bound on its diameter. The results are of interest as they can be used in the study of communication properties of real networks, in particular for dynamical processes taking place on them (broadcasting, network synchronization, virus spreading, etc.).