We consider a set of scalar conservation laws on a graph. Based on a choice of stationary states of the problem – analogous to the constants in Kruzkhov's entropy condition – we establish the uniqueness and stability of entropy solutions. For two classes of flux functions – either monotone or concave fluxes – we establish the convergence of an easy-to-implement Engquist–Osher-type finite volume method. This is joint work with Markus Musch and Nils Henrik Risebro (University of Oslo).