Urban water systems are composed of subsystems (gully pots, storm sewers and surface water), each with its own system dynamics. Engineers balance the functioning of the systems based on storage and discharge capacity of the subsystems. The load on, and capacity are influenced by e.g. ageing, urbanization, climate change. Consequently, the performance of and demand put on subsystems varies over time, potentially resulting in disturbances in the balance between the storage and discharge capacity of the subsystems. The Graph Based Weakest Link Method (GBWLM) is developed to analyse the behaviour of urban water systems to identify potential limitations due to deterioration, and/or changes in load. The proposed GBWLM is based on the structure of the networks. In addition, Graph theory is applied as alternative for series of hydraulic calculations. The GBWLM allows for an integrated performance assessments of urban water systems using multi-decades rainfall series. The results are sufficiently accurate to be able to determine the extent and frequency of urban flooding in order to compare the performance of the subsystems for various degrees of available discharge capacity. Keywords Criticality, flow paths analysis, Graph theory, linearised hydrodynamics, urban water systems, Weakest Link Method Highlights 1. Method for the analysis of urban water systems based on Graph theory 2. The use of linearised hydrodynamics in flow path analyses