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To mitigate urban drainage network pressures and seek sustainable solutions, novel tools like graph theory are presently being studied. This paper presents a systematic literature review of graph-based approaches through an intensive content analysis based on 144 published papers. Comparisons are drawn between water distribution networks and urban drainage networks in terms of convergence and divergence, revealing more divergence in network topological characteristics but more convergence in functional features. The findings provide convincing evidence for applications in UDNs, despite limited numbers and depth. Subsequently, a comparison between graph-based and hydraulic-based approaches is shown, demonstrating distinct advantages of graph-based methods in cases with limited data and time constraints. Based on these findings, the paper suggests several potential directions, including the improvement of parameter calculation formulas, the definition of parameter mathematical ranges and the popularization of recommended values. Finally, the paper examines its own shortcomings.

The role of graph-based methods in urban drainage networks (UDNs): review and directions for future