Robustness and Vulnerability Analysis of Water Distribution Networks Using Graph Theoretic and Complex Network Principles
Alireza Z. K. Yazdani, Paul J. Jeffrey · 2011
Water distribution systems are regarded as large sparse graphs with complex network characteristics. Topological aspects of system resilience, viewed as the antonym to structural vulnerability, are assessed in connection with the network architecture, robustness and loop redundancy. Deterministic techniques from complex networks and spectral graph theory are utilized to quantify well-connectedness and estimate loop redundancy in the studied benchmark networks. By using graph connectivity and expansion properties, system robustness against node/link failures and isolation of the demand nodes from the source(s) are assessed and network tolerance against random failures and targeted attacks on their bridges and cut sets are analyzed. Among other measurements, two metrics of meshed-ness and algebraic connectivity are proposed as candidates for quantification of redundancy and robustness, respectively, in optimization design models. A brief discussion on the scope and relevance of the provided measurements in the analysis of resilience of water distribution networks is presented.