Underground water infrastructure is essential for life in cities. The aging of these infrastructures requires maintenance strategies to maintain a minimum service level. Not all elements are equally important for the functioning of the infrastructure as a whole. Identifying the most critical elements in a network is crucial for formulating asset management strategies. The graph theory is presented as a means to identify the most critical elements in a network with respect to malfunctioning of the system as a whole. As opposed to conventional methods, the proposed method does not rely on iterative hydraulic calculations; instead, the structure of the network is taken as a starting point. In contrast to methods applied in practise, the results are independent on the chosen test-load. Because of the limited calculation effort, the method allows the analysis of large networks that are now, for practical reasons, beyond the scope of methods applied so-far.