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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 networks robustness vs link removal strategies after small fraction of links removed. The robustness R of the functioning measurements Eff, LCC and TF after q = 5, 10, and 15% removed links for each links attack strategy for each real-world networks analyzed. The network robustness is normalized by the max robustness for that system functioning measure. The lower is R, the higher is the efficacy of that link attack strategy to damage the network. Link removal strategies: random (Ran), strong (Str), weak (We), link weighted betwenness centrality (BCw), link binary betwenness centrality (BC), end nodes end nodes degree product (DP), end nodes betwenness centrality product (BPw), end nodes betwenness centrality product (BPw), end nodes strength product (SP), end nodes binary transitivity product (TP), end nodes weighted transitivity product (TPw).