Quantitative Study on Vulnerability of Water Supply System Based on Complex Network and Fractal Theory

Vulnerability assessment of water distribution networks (WDNs) is essential for supply reliability and resilience to disruptions. Conventional methods often overlook pipeline physical heterogeneity, multiscale topological complexity, and failure propagation uncertainty, yielding incomplete risk profiles. This study proposes an integrated framework combining complex network theory, refined fractal analysis, and Shannon entropy. A modified Simplified Fractal Index is proposed, adapting head/tail breaks to emphasize hydraulically dominant large-scale pipelines and incorporating attribute weighting, better capturing heavy-tailed distributions in length, elevation, and demand. Pipe rupture probability is modeled through pipeline length and diameter and then fused with edge betweenness centrality and fractal scaling to derive physically grounded risk weights. Shannon entropy normalization of the risk distribution produces a global vulnerability index that effectively captures risk concentration under random failure scenarios. Benchmark analyses, including modularity and metric comparisons, validate the framework’s ability to reveal interactions among community structure, geography, and risk patterns. Complementary hydraulic simulations under Monte Carlo random pipe failures confirm moderate alignment between vulnerability index/entropy and functional performance (pressure-deficient nodes), validating the framework as an efficient prescreening tool. The methodology provides practical guidance for network design and management, identifying critical components and promotion of balanced modular configurations. This scalable approach enhances WDN resilience assessment, with promising extensions to dynamic simulations and additional physical attributes.