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. 2020 Oct 27;10:18387. doi: 10.1038/s41598-020-75147-w

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© The Author(s) 2020

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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Left panel: complex network with $N = 500$ nodes, generated using the ER model with connection probability $p = 0.9$ (graph generated with Gephi 0.9.2³⁹). Central panel: shifted graph spectrum $E_{n}$ (red horizontal lines) and reconstructed potential V(x) (green, only positive x displayed) corresponding to the network in the left panel, with x the dimensionless variable of the Schrödinger equation (4). Right panel: ensemble potential $V_{m} (x)$ over $M = 100$ network realizations with the same N and p.