We provide an interpretation of the discrete version of Morse inequalities, following
Witten’s approach via supersymmetric quantum mechanics (J. Differential Geom.17:4 (1982), 661-692), adapted by Forman to finite graphs, as a particular
instance of Morse–Witten theory for cell complexes (Topology 37:5 (1998), 945–979).
We describe the general framework of graph quantum mechanics and we produce
discrete versions of the Hodge theorems and energy cut-offs within this
formulation.