Abstract : we consider Schrödinger operators on a class of
periodic quantum graphs with randomly distributed Kirchhoff
coupling constants at all vertices. Using the technique of
self-adjoint extensions and finite volume localization
criteria for discrete random Schrödinger operators, we obtain
conditions for localization on quantum graphs in terms of
finite volume criteria for some energy-dependent discrete
Hamiltonians. This is then applied to large coupling and band
edge localization.