We prove a Feynman path integral formula for the unitary group exp(−itLv,θ), t≥0, associated with a discrete magnetic Schrödinger operator Lv,θ on a large class of weighted infinite graphs. As a consequence, we get a new Kato-Simon estimate
|exp(−itLv,θ)(x,y)|≤exp(−tL−deg,0)(x,y),
which controls the unitary group uniformly in the potentials in terms of a Schrödinger semigroup, where the potential deg is the weighted degree function of the graph.
