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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 non identical layers. 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 the inter-layer coupling strength λ = 0.23 for mixed ER (ESE, empty circles) and mixed SF (SES, empty squares) layer configurations. The relay lines are disconnected following a descending order of the outer node degrees and for comparison the corresponding values for identical layers -see Fig. 6(b) are plotted in solid symbols. The red solid (ESE) and empty (SES) triangles show the behavior when the relay lines are disconnected following the degree ranking of the relay layer.