6963 eng reportzib 0 -- 2018-07-25 -- All feasible flows in potential-driven networks induce an orientation on the undirected graph underlying the network. Clearly, these orientations must satisfy two conditions: they are acyclic and there are no "dead ends" in the network, i.e. each source requires outgoing flows, each sink requires incoming flows, and each transhipment vertex requires both an incoming and an outgoing flow. In this paper we will call orientations that satisfy these conditions acyclic source-transhipment-sink orientations (ASTS-orientation) and study their structure. In particular, we characterize graphs that allow for such an orientation, describe a way to enumerate all possible ASTS-orientations of a given graph, present an algorithm to simplify and decompose a graph before such an enumeration and shed light on the role of zero flows in the context of ASTS-orientations. 1438-0064 urn:nbn:de:0297-zib-69632 Kai-Helge Becker Benjamin Hiller Benjamin Hiller 18-31 OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING Mathematical Optimization MODAL-GasLab MODAL-Gesamt ECMATH-MI10 Applied Optimization https://opus4.kobv.de/opus4-zib/files/6963/ZR-18-31ZIB.pdf