Investigating critical node identification in water networks through distance Laplacian energy centrality

Identifying influential nodes in water distribution networks is essential for ensuring efficient and reliable operations. This paper introduces a novel centrality measure called distance Laplacian energy centrality (DLC), designed to evaluate node importance by combining the network's topological structure and hydraulic properties into a unified framework. The DLC measure quantifies the criticality of a node by assessing its influence on the network's Laplacian energy, which represents the network's characteristics, and distance metrics that reflect how the removal of the node affects network connectivity and flow. The DLC is applied to real-world water distribution networks and compared with traditional centrality measures such as betweenness, degree, closeness, eigenvector, and Laplacian centrality. By analyzing the effect of node deletion on graph connectivity, the DLC measure offers a more precise identification of critical nodes. Extensive experiments conducted on four heterogeneous water networks validate that DLC not only surpasses traditional measures in performance but also increases robustness and optimized network functionality. The experiments showed that the networks are strengthened based on critical nodes identified by DLC which demonstrated significant improvements in connectivity. The comparative analysis using statistical plots and charts reveals the power of the DLC technique in efficient water flow and reducing vulnerability to disruptions compared to traditional measures. The results confirm that DLC effectively captures both local and global properties of the network, providing greater precision in identifying influential nodes to ensure optimal water flow and reliability. Moreover, DLC's superiority in pinpointing critical nodes with greater accuracy reinforces its utility over existing methods.