Hierarchical structure analysis of water distribution networks coupling pipeline dual graph and infomap algorithm

Water distribution networks (WDNs) are essential urban infrastructure networks that play a crucial role in maintaining the stability and well-being of a city's residents. Meanwhile, effective structural feature extraction and partitioning plays a vital role in optimizing water supply operations. However, WDNs possess a complex network structure constrained by geography and a large scale. Understanding the hierarchical structure of WDNs through network science algorithms remains challenging. Additionally, simplifying the expression of the network structure is an urgent concern. In this paper, to solve the previously raised issues, we propose a hierarchical community mining method that applies Infomap algorithm partitioning in a hierarchical procedure. This method combines the Pipeline Dual Graph (PDG) model with the Infomap algorithm. The PDG model is constructed and then, the Infomap algorithm is used to construct randomized travel paths and group coding rules to solve the minimum coding length and find the optimal network multi-level partition. Experimental results demonstrate that the PDG model effectively simplifies the representation of the network structure and has obvious scale-free characteristics. In addition, the results show that the node distribution is more even. More importantly, this method can effectively reduce the number of partitions while maintaining the modular performance of networks.