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Open AccessFeature PaperArticle

Scaling-Laws of Flow Entropy with Topological Metrics of Water Distribution Networks

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Dipartimento di Ingegneria Civile, Design, Edilizia e Ambiente, Università degli Studi della Campania “Luigi Vanvitelli”, via Roma 29, 81031 Aversa, Italy
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Action Group CTRL+SWAN of the European Innovation Partnership on Water, EU, B-1049 Brussels, Belgium
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Author to whom correspondence should be addressed.
Entropy 2018, 20(2), 95; https://doi.org/10.3390/e20020095
Received: 28 December 2017 / Revised: 24 January 2018 / Accepted: 26 January 2018 / Published: 30 January 2018
(This article belongs to the Special Issue Entropy Applications in Environmental and Water Engineering)
Robustness of water distribution networks is related to their connectivity and topological structure, which also affect their reliability. Flow entropy, based on Shannon’s informational entropy, has been proposed as a measure of network redundancy and adopted as a proxy of reliability in optimal network design procedures. In this paper, the scaling properties of flow entropy of water distribution networks with their size and other topological metrics are studied. To such aim, flow entropy, maximum flow entropy, link density and average path length have been evaluated for a set of 22 networks, both real and synthetic, with different size and topology. The obtained results led to identify suitable scaling laws of flow entropy and maximum flow entropy with water distribution network size, in the form of power–laws. The obtained relationships allow comparing the flow entropy of water distribution networks with different size, and provide an easy tool to define the maximum achievable entropy of a specific water distribution network. An example of application of the obtained relationships to the design of a water distribution network is provided, showing how, with a constrained multi-objective optimization procedure, a tradeoff between network cost and robustness is easily identified. View Full-Text
Keywords: scaling laws; power laws; water distribution networks; robustness; flow entropy scaling laws; power laws; water distribution networks; robustness; flow entropy
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MDPI and ACS Style

Santonastaso, G.F.; Di Nardo, A.; Di Natale, M.; Giudicianni, C.; Greco, R. Scaling-Laws of Flow Entropy with Topological Metrics of Water Distribution Networks. Entropy 2018, 20, 95.

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