In this paper, we analyze the leak localization problem in potential flow networks. We present a general model encompassing various physical systems, for example, water distribution networks. In contrast to conventional water distribution network models, our model is neither restricted to any particular type of potential loss function nor to vertex leaks. We consider leak localization via vertex potential analysis, a general description of methods that work by comparing vertex potentials calculated under a leak location hypothesis to measured vertex potentials. We derive conditions on the graph structure of the network and the potential sensor placement, under which it is guaranteed that the leak can be limited, via vertex potential analysis, to a small set of locations. We suggest a bisection method to utilize our conditions. Our conditions are based on one-way edges in graphs, a concept that we introduce. In extension, our results can be used for sensor placement.