In the last few years, water utilities have recognized the importance of evaluating the safety of water distribution networks from the potential risks of contamination, arising from failures or from intentional (targeted) or random attacks. Research literature has been recently focused on the optimal design of efficient detection systems, generally expressed as the problem of the optimal placement of monitoring sensors. In this paper, we introduce a methodology for calculating an index of vulnerability that represents the tendency of an injected contaminant to spread over the network. Epanet quality simulations are performed in order to determine the distribution function of the number of potentially contaminated nodes. The results show how such distribution is overall fitted by a stretched exponential law. The comparison with an auto-similar, tree-like network (described by a power-law) allows the determination of the Vulnerability Index, which quantifies how “far” the behavior of a given system deviates from pure scale-freeness. It is analytically calculated by a two-fold approximation of the stretched exponential and provides an alternative way of evaluating robustness against random water contamination. Different networks can then be directly compared, in order to assess and prioritize control measures and interventions.
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