Let X be a countable infinite set which carries the structure of a weighted graph, which is even allowed to be locally infinite. Given an electric potential v on X and a magnetic potential \theta on X one can canonically contsruct a magnetic Schrödinger operator H(v,\theta) on the Hilbert space of square integrable functions on X. The aim of this talk is to explain a probabilistic formula for the Euclidean path integral

corresponding to exp(-t H(v,\theta)), t>0. In contrast to the continuum situation, this formula also has a well-defined variant for the “non-Euclidean” path integral for exp(-it H(v,\theta)), t>0.