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. 2017 Nov 8;7:15059. doi: 10.1038/s41598-017-14384-y

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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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Two random regular (RR) networks with P _A(k) = P _B(k) = δ _k,5 and P _sA(k) = P _sB(k) = δ _k,5 and system size N = 10⁵ for different values of required supplies, $k_{s X}^{⁎}$ = 1 (○), $k_{s X}^{⁎}$ = 2 (), $k_{s X}^{⁎}$ = 3 (), $k_{s X}^{⁎}$ = 4 (), as a function of the initial fraction of survived nodes p. Also shown two RR networks with P _A(k) = P _B(k) = δ _k,5, but P _sA(k) = P _sB(k) = δ _k,1, $k_{s X}^{⁎}$ = 1 (). The symbols are the results of the stochastic simulations and the lines are the iterated values obtained by equations (3–5). The dashed-dotted lines represent only the theoretical results since they have been obtained in Ref.¹¹. In panels (a) and (b) we show the order parameter of network A and B, μ _A and μ _B, respectively for the giant component rule.

Inline graphic — Two random regular (RR) networks with P _A(k) = P _B(k) = δ _k,5 and P _sA(k) = P _sB(k) = δ _k,5 and system size N = 10⁵ for different values of required supplies, $k_{s X}^{⁎}$ = 1 (○), $k_{s X}^{⁎}$ = 2 (), $k_{s X}^{⁎}$ = 3 (), $k_{s X}^{⁎}$ = 4 (), as a function of the initial fraction of survived nodes p. Also shown two RR networks with P _A(k) = P _B(k) = δ _k,5, but P _sA(k) = P _sB(k) = δ _k,1, $k_{s X}^{⁎}$ = 1 (). The symbols are the results of the stochastic simulations and the lines are the iterated values obtained by equations (3–5). The dashed-dotted lines represent only the theoretical results since they have been obtained in Ref.¹¹. In panels (a) and (b) we show the order parameter of network A and B, μ _A and μ _B, respectively for the giant component rule.