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. 2017 Jun 12;7:3268. doi: 10.1038/s41598-017-03379-4

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© The Author(s) 2017

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 expectation of the number of immunized nodes E[w] from the theoretical estimations and the immunization simulations in (a) the Advogato network, (b) the Brightkite network, (c) the Epinions network and (d) the MSM network. The expectation is averaged over 100 simulations.