Reconstructing Sewer Network Topology Using Graph Theory

To manage sewer networks, reliable data is needed, which is often challenging. This study proposes a novel methodology to reconstruct the sewer network topology using graph theory. Two core procedures—flow adjustment and edge addition—re-establish hydraulically consistent flow paths and restore connectivity in disconnected portions of the network by reversing and adding links. The proposed approach operates at the pipe level, repairing directional reachability. It leverages only the existing network topology to reconstruct connectivity, guided by the principle that every node must have a downstream path to an outlet. The methodology is first applied to reconstruct the sewer network of Montpellier Metropolis in the South of France. Then it is validated by deliberately removing and reversing edges and applying the algorithms to test the methodology’s capability in recovering the correct topology. Both methods performed well individually, especially at lower percentages of reversal (1%) and removal (1%), with a correctness of 0.99 for flow adjustment and 0.8 for edge addition. Although the results were poorer when combining the methods and increasing data degradation—particularly at 10% reversal and 10% removal (correctness of 0.64)—the methodology continued to produce a functionally consistent and logically coherent network, highlighting its robustness given the absence of supporting attribute data.