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. 2018 Jun 5;8:8629. doi: 10.1038/s41598-018-26945-w

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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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Structural robustness of the network relay synchronization for identical layers. (a) Synchronization error between the outer layers E_−1,1 vs the decreasing number of connected relay lines for identical ER (blue empty symbols) and SF (black solid symbols) layers. Relay lines are disconnected following a descending (circle symbols) or ascending (square symbols) node degree ranking of the outer layers (seed legend in (b)). Parameter values are N = 500, 〈k〉 = 8, λ = 0.23 and σ₀ = σ₁ = 0.8. (b) Number of multiplexed relay lines needed to support a relay network state as a function of the intra-layer coupling strength σ₀ = σ₁ while keeping constant λ = 0.23. The different curves are explained in the legend. All the results are averaged over 10 different network realizations.