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. 2020 Feb 24;10:3297. doi: 10.1038/s41598-020-60151-x

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© The Author(s) 2020

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(left) Standard edge betweenness for a water supply network. Source and demand nodes have the same intrinsic relevance equal to 1. The edge betweenness is identified by colored edges ranging from black (maximum value) to cyan (minimum value). The most important pipe is the number 4. (right) Proposed edge betweenness embedding the intrinsic relevance in terms of demand for each node and as sum of demands for the source node (values in l/s are reported close to each node). The pipe 34 results the most important edge.