Enhancing resilience of drainage networks is a crucial practice to protect both humans and nature. One way to enhance resilience is to identify critical parts of drainage networks for targeted management and maintenance strategies. While hydrodynamic modelling approaches for identification are computationally intensive, in this study, a novel method based on complex network analysis is used to determine the most critical pipes in a benchmark and a real network of an Alpine municipality. For evaluation, the results of the proposed graph method are compared with hydrodynamic simulations in terms of accuracy and computational time. Results show that the proposed method is very accurate (R2 = 0.98) for branched benchmark network while the accuracy reduces slightly for the more complex real network (R2 = 0.96). Furthermore, the accuracy of the proposed method decreases with increasing loop degree and when the system is pressured with higher return period rainfall. Although the outcomes of the proposed method show slight differences to hydrodynamic modelling, it is still very useful because the computational time and data required are much less than a hydrodynamic model.