This chapter is devoted to various interactions between the graph theory and mathematical physics of disordered media, studying spectral properties of random quantum Hamiltonians. We show how the notions, methods, and constructions of graph theory can help one to solve difficult problems, and also highlight recent developments in spectral theory of multiparticle random Hamiltonians which both benefit from graph‐theoretical methods and suggest original structures where new insights are required from various areas of mathematical physics in a broad sense.
Part of the book: Graph Theory