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. 2021 May 16;82(7):61. doi: 10.1007/s00285-021-01609-y

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© The Author(s) 2021

Open AccessThis 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 licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence 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 licence, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 10 — Comparing regular graphs that construct amplifiers (cubic graphs as green line, quartic graphs as red line) with graphs that do not (cubic graphs as magenta line, quartic graphs as blue line). a The spectral distance measure $d (G, G^{'})$ defined by Eq. (13) on logarithmic scale. b The averaged von Neumann entropy $S_{G}$ defined by Eq. (14)