A complex network approach to robustness and vulnerability of spatially organized water distribution networks

TL;DR

This paper models water distribution networks as complex planar graphs to analyze their robustness and vulnerability using spectral graph theory, proposing new metrics for system resilience and redundancy.

Contribution

It introduces graph-theoretic metrics like meshed-ness and algebraic connectivity to quantify robustness and redundancy in water networks, linking topology to system resilience.

Findings

Metrics effectively quantify network robustness and redundancy.

Networks show varying vulnerability to targeted attacks and random failures.

Proposed measures assist in optimizing water distribution system design.

Abstract

In this work, water distribution systems are regarded as large sparse planar graphs with complex network characteristics and the relationship between important topological features of the network (i.e. structural robustness and loop redundancy) and system resilience, viewed as the antonym to structural vulnerability, are assessed. 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 limitations of the provided measurements in the analysis of operational reliability of water distribution systems is presented.