On the robustness of potential-based flow networks

Abstract Potential-based flows provide a simple yet realistic mathematical model of transport in many real-world infrastructure networks such as, e.g., gas or water networks, where the flow along each edge depends on difference potentials at its end nodes. We call network topology robust if maximal node potential needed to satisfy set demands never increases when are decreased. This notion robustness is motivated by users first make reservations for certain that may be larger than actual sent later on. In these correspond physical quantities as pressures hydraulic heads and must guaranteed lie within fixed range, even amounts smaller previously reserved demands. Our main results precise characterization topologies case point-to-point via forbidden node-labeled graph minors, well an efficient algorithm testing robustness.