  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.
