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Potential energy of complex networks: a quantum mechanical perspective

We propose a characterization of complex networks, based on the potential of an associated Schrödinger equation. The potential is designed so that the energy spectrum of the Schrödinger equation coincides with the graph spectrum of the normalized Laplacian. Crucial information is retained in the rec...

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Autores principales: Amoroso, Nicola, Bellantuono, Loredana, Pascazio, Saverio, Lombardi, Angela, Monaco, Alfonso, Tangaro, Sabina, Bellotti, Roberto
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group UK 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7592062/
https://www.ncbi.nlm.nih.gov/pubmed/33110089
http://dx.doi.org/10.1038/s41598-020-75147-w
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author Amoroso, Nicola
Bellantuono, Loredana
Pascazio, Saverio
Lombardi, Angela
Monaco, Alfonso
Tangaro, Sabina
Bellotti, Roberto
author_facet Amoroso, Nicola
Bellantuono, Loredana
Pascazio, Saverio
Lombardi, Angela
Monaco, Alfonso
Tangaro, Sabina
Bellotti, Roberto
author_sort Amoroso, Nicola
collection PubMed
description We propose a characterization of complex networks, based on the potential of an associated Schrödinger equation. The potential is designed so that the energy spectrum of the Schrödinger equation coincides with the graph spectrum of the normalized Laplacian. Crucial information is retained in the reconstructed potential, which provides a compact representation of the properties of the network structure. The median potential over several random network realizations, which we call ensemble potential, is fitted via a Landau-like function, and its length scale is found to diverge as the critical connection probability is approached from above. The ruggedness of the ensemble potential profile is quantified by using the Higuchi fractal dimension, which displays a maximum at the critical connection probability. This demonstrates that this technique can be successfully employed in the study of random networks, as an alternative indicator of the percolation phase transition. We apply the proposed approach to the investigation of real-world networks describing infrastructures (US power grid). Curiously, although no notion of phase transition can be given for such networks, the fractality of the ensemble potential displays signatures of criticality. We also show that standard techniques (such as the scaling features of the largest connected component) do not detect any signature or remnant of criticality.
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spelling pubmed-75920622020-10-29 Potential energy of complex networks: a quantum mechanical perspective Amoroso, Nicola Bellantuono, Loredana Pascazio, Saverio Lombardi, Angela Monaco, Alfonso Tangaro, Sabina Bellotti, Roberto Sci Rep Article We propose a characterization of complex networks, based on the potential of an associated Schrödinger equation. The potential is designed so that the energy spectrum of the Schrödinger equation coincides with the graph spectrum of the normalized Laplacian. Crucial information is retained in the reconstructed potential, which provides a compact representation of the properties of the network structure. The median potential over several random network realizations, which we call ensemble potential, is fitted via a Landau-like function, and its length scale is found to diverge as the critical connection probability is approached from above. The ruggedness of the ensemble potential profile is quantified by using the Higuchi fractal dimension, which displays a maximum at the critical connection probability. This demonstrates that this technique can be successfully employed in the study of random networks, as an alternative indicator of the percolation phase transition. We apply the proposed approach to the investigation of real-world networks describing infrastructures (US power grid). Curiously, although no notion of phase transition can be given for such networks, the fractality of the ensemble potential displays signatures of criticality. We also show that standard techniques (such as the scaling features of the largest connected component) do not detect any signature or remnant of criticality. Nature Publishing Group UK 2020-10-27 /pmc/articles/PMC7592062/ /pubmed/33110089 http://dx.doi.org/10.1038/s41598-020-75147-w Text en © 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/.
spellingShingle Article
Amoroso, Nicola
Bellantuono, Loredana
Pascazio, Saverio
Lombardi, Angela
Monaco, Alfonso
Tangaro, Sabina
Bellotti, Roberto
Potential energy of complex networks: a quantum mechanical perspective
title Potential energy of complex networks: a quantum mechanical perspective
title_full Potential energy of complex networks: a quantum mechanical perspective
title_fullStr Potential energy of complex networks: a quantum mechanical perspective
title_full_unstemmed Potential energy of complex networks: a quantum mechanical perspective
title_short Potential energy of complex networks: a quantum mechanical perspective
title_sort potential energy of complex networks: a quantum mechanical perspective
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7592062/
https://www.ncbi.nlm.nih.gov/pubmed/33110089
http://dx.doi.org/10.1038/s41598-020-75147-w
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