For the management of piped infrastructure (e.g. water supply networks, gas distribution systems) strategies are required to program the maintenance activities (e.g. repairs, replacement). In general, these activities are based on risk management that combines the probability and consequences of failure. In this paper a method is proposed to quickly identify the most critical elements in a network with respect to malfunctioning of a system as a whole. As opposed to methods applied so far, this method does not rely on iterative hydraulic calculations but takes the structure of the network as a starting point and is based on Graph theory. First the theory of the method is presented, secondly the first results are presented based on a water supply network and the outcomes are compared with traditional methods applied so far. Finally, the results are discussed and conclusions are formulated.