Water distribution systems (WDSs) are complex networks with numerous interconnected junctions and pipes. The robustness and reliability of these systems are critically dependent on their network structure, necessitating detailed analysis for proactive leak detection to maintain integrity and functionality. This study addresses gaps in traditional WDS analysis by integrating hydraulic measures with graph theory to improve sensitivity analysis for leak detection. Through case studies of five distinct WDSs, we investigate the relationship between hydraulic measures and graph theory metrics. Our findings demonstrate the collective impact of these factors on leak detection and system efficiency. The research provides enhanced insights into WDS operational dynamics and highlights the significant potential of graph theory to bolster network resilience and reliability.