This fascinating volume investigates the structure of eigenvectors and looks at the number of
their sign graphs (nodal domains) Perron components and graphs with extremal properties with
respect to eigenvectors. The Rayleigh quotient and rearrangement of graphs form the main
methodology. Eigenvectors of graph Laplacians may seem a surprising topic for a book but the
authors show that there are subtle differences between the properties of solutions of
Schrödinger equations on manifolds on the one hand and their discrete analogs on graphs.
