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. 2019 Jul 23;9:10692. doi: 10.1038/s41598-019-47119-2

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© The Author(s) 2019

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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The real-world complex networks robustness of the efficiency functioning (Eff) decreases with links weight heterogeneity where instead the LCC is approximately constant. The robustness of the efficiency Eff and largest connected cluster LCC measures of the system functioning under nodes and links removal strategies. We randomly assigned the weight of the links over the real-world topological structure of the networks under exam. Link weights are sorted from 2 values distribution (1, Wmax); the upper limit Wmax ranges in (1, 10⁵); the outcomes are the average of 10⁴ simulations. For sake of example we depict the outcomes from the Cargo ship and the E. coli network. Left column: Cargo ship network under nodes removal strategies; Right column: E. Coli network under links removal strategies.