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. 2020 Mar 3;10:3911. doi: 10.1038/s41598-020-60298-7

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© The Author(s) 2020

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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Real-world complex weighted networks functioning decrease (Eff & LCC) under 5, 10, 15% of links removed. The system functioning is depicted under link removal for the three most harmful link attack strategies, e.g. Strong, BCw and SP. The system functioning is normalized by the initial functioning value (e.g. before any removal). The pink area depicts the difference between Eff and LCC measures along the link removal process. For all networks except Net, under BCw and SP link removal strategies, after small fraction of links removed we observe a quick efficiency (Eff) decrease whereas the largest connected cluster (LCC) decreases very slowly.