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Article

A Novel Graph-Based Vulnerability Metric in Urban Network Infrastructures: The Case of Water Distribution Networks

1
Department of Computer Science, Systems and Communication, University of Milano-Bicocca, 20126 Milan, Italy
2
Department of Economics, Management and Statistics, University of Milano-Bicocca, 20126 Milan, Italy
*
Author to whom correspondence should be addressed.
Academic Editors: Francesco De Paola and Stefano Alvisi
Water 2021, 13(11), 1502; https://doi.org/10.3390/w13111502
Received: 13 April 2021 / Revised: 20 May 2021 / Accepted: 25 May 2021 / Published: 27 May 2021
(This article belongs to the Section Urban Water Management)
The key contribution of this paper is to embed the analysis of the network in a framework based on a mapping from the input space whose elements are nodes of a graph or the entire graph into an information space whose elements are probability distributions associated to objects in the input space. Specifically, a node is associated to the probability distribution of its node-to-node distances and the whole graph to the aggregation of these node distributions. In this space two distances are proposed for this analysis: Jensen-Shannon and Wasserstein, based respectively on information theory and optimal transport theory. This representation allows to compute the distance between the original network and the one obtained by the removal of nodes or edges and use this distance as an index of the increase in vulnerability induced by the removal. In this way a new characterization of vulnerability is obtained. This new index has been tested in two real-world water distribution networks. The results obtained are discussed along those which relate vulnerability to the loss of efficiency and those given by the analysis of the spectra of the adjacency and Laplacian matrices of the network. The models and algorithms considered in this paper have been integrated into an analytics framework which can also support the analysis of other networked infrastructures among which power grids, gas distribution, and transit networks are included. View Full-Text
Keywords: network analysis; robustness; water distribution network; spectral analysis; Jensen-Shannon divergence; Wasserstein distance network analysis; robustness; water distribution network; spectral analysis; Jensen-Shannon divergence; Wasserstein distance
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MDPI and ACS Style

Ponti, A.; Candelieri, A.; Giordani, I.; Archetti, F. A Novel Graph-Based Vulnerability Metric in Urban Network Infrastructures: The Case of Water Distribution Networks. Water 2021, 13, 1502. https://doi.org/10.3390/w13111502

AMA Style

Ponti A, Candelieri A, Giordani I, Archetti F. A Novel Graph-Based Vulnerability Metric in Urban Network Infrastructures: The Case of Water Distribution Networks. Water. 2021; 13(11):1502. https://doi.org/10.3390/w13111502

Chicago/Turabian Style

Ponti, Andrea, Antonio Candelieri, Ilaria Giordani, and Francesco Archetti. 2021. "A Novel Graph-Based Vulnerability Metric in Urban Network Infrastructures: The Case of Water Distribution Networks" Water 13, no. 11: 1502. https://doi.org/10.3390/w13111502

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