Revealing critical pipes in water networks through integrated edge centrality and multi-criteria vulnerability analysis

Water distribution networks (WDNs) are critical infrastructure that must reliably supply water despite aging components and frequent pipe failures. Traditional vulnerability assessments largely adopt a node-centric perspective, often overlooking the pivotal role of pipelines themselves. This study proposes a paradigm shift to a pipe-centric vulnerability assessment framework that integrates complex network theory with multi-criteria analysis. We treat pipes as fundamental network elements and develop edge centrality metrics (ECMs) tailored to pipe characteristics. Sixteen distinct ECMs are generated by incorporating pipe length, a condition index (CI), and probability of failure (POF) into four base topological metrics (edge degree, edge neighborhood degree, edge betweenness, edge closeness). These metrics capture both network connectivity importance and physical deterioration risk. The entropy weight method (EWM) objectively assigns weights to each metric, and the technique for order preference by similarity to ideal solution (TOPSIS) aggregates them into a composite vulnerability index (VI) that ranks pipe criticality. The framework is demonstrated on Hong Kong's freshwater (FW) and saltwater (SW) networks. Results show that fewer than 5 % of pipes are classified as highly vulnerable; notably, FW Zone A contains the highest fraction of high-VI pipes (≈14 %), reflecting its older infrastructure and dense population. The VI effectively identifies critical pipes, as removing the top 0.4 % most vulnerable pipes dramatically drops network connectivity (over 70 % reduction in a key performance measure). These findings highlight the value of a pipe-centric vulnerability approach and offer practical insights for optimizing maintenance and rehabilitation strategies in urban water networks.