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. 2020 Jan 9;10:73. doi: 10.1038/s41598-019-56704-4

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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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The figure shows the fragmentation process. In the left panel (A), the inset figure shows the size of the largest strongly connected component as a function of the fraction of nodes removed according to the best topological attack (HB_sA - blue curve), the mean and error bars for a 1,000 random attacks (red curve, Rnd), and the real police intervention result (black diamond shape, DN). In this case the network only breaks completely after 60% of removals. The main figure shows a zoom in near the real police intervention which resulted in a 23% decrease of the strongly connected component, while the topological attack resulted in a 37% breakdown (1.6 times more efficient). The right panel (B) shows the same process but now considering the relative size of the largest connected component (regardless of strong and weak components). Note that in this case even the best topological attack (high in-degree adaptive attack, H_iDA) in the region that real police intervention took place is as good as random and the network only breaks after almost 80% of disruption.