The aim of this work is to study the controllability of the bilinear Schrodinger equation on compact graphs. In particular, we consider the equation (BSE) i partial derivative(t)psi = -Delta psi + u(t) B psi in the Hilbert space L-2 (G, C), with G being a compact graph. The Laplacian -Delta is equipped with self-adjoint boundary conditions, B is a bounded symmetric operator, and u is an element of L-2((0, T), R) with T > 0. We provide a new technique leading to the global exact controllability of (BSE) in D(vertical bar Delta vertical bar(s/2)) with s >= 3. Afterwards, we introduce the "energetic controllability," a weaker notion of controllability useful when the global exact controllability fails. In conclusion, we develop some applications of the main results involving, for instance, star graphs.