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. 2018 Sep 10;8:13513. doi: 10.1038/s41598-018-31902-8

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© The Author(s) 2018

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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Example network (left) and its robustness curves (right). The network lesmis consists of 77 nodes and 254 links. The average degree is 6.597. The competitors in our study reveal very distinct attacking strategies and percolation thresholds for the network. In the legend, all methods are ordered by increasing value of R, see Eq. (1). The range of R is between 0.09 and 0.21, which shows the importance of selecting an appropriate attacking strategy for a given network.