  This thesis generalizes the differential operators on standard oriented
graphs and oriented hypergraphs introduced in 10.1137/15M1022793 and
arXiv:2007.00325. The extended concepts of gradients, adjoints and
$p$-Laplacians for vertices and (hyper)arcs include novel parametrization
possibilities, while simultaneously fulfilling expected properties of the
continuum setting, which are not granted by current definitions.
