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Beyond preferential attachment: falling of stars and survival of superstars

Numerous studies over the past decades established that real-world networks typically follow preferential attachment and detachment principles. Subsequently, this implies that degree fluctuations monotonically increase while rising up the ‘degree ladder’, causing high-degree nodes to be prone for at...

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Autores principales: Somin, Shahar, Altshuler, Yaniv, ‘Sandy’ Pentland, Alex, Shmueli, Erez
Formato: Online Artículo Texto
Lenguaje:English
Publicado: The Royal Society 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9399691/
https://www.ncbi.nlm.nih.gov/pubmed/36039282
http://dx.doi.org/10.1098/rsos.220899
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author Somin, Shahar
Altshuler, Yaniv
‘Sandy’ Pentland, Alex
Shmueli, Erez
author_facet Somin, Shahar
Altshuler, Yaniv
‘Sandy’ Pentland, Alex
Shmueli, Erez
author_sort Somin, Shahar
collection PubMed
description Numerous studies over the past decades established that real-world networks typically follow preferential attachment and detachment principles. Subsequently, this implies that degree fluctuations monotonically increase while rising up the ‘degree ladder’, causing high-degree nodes to be prone for attachment of new edges and for detachment of existing ones. Despite the extensive study of node degrees (absolute popularity), many domains consider node ranks (relative popularity) as of greater importance. This raises intriguing questions—what dynamics are expected to emerge when observing the ranking of network nodes over time? Does the ranking of nodes present similar monotonous patterns to the dynamics of their corresponding degrees? In this paper, we show that surprisingly the answer is not straightforward. By performing both theoretical and empirical analyses, we demonstrate that preferential principles do not apply to the temporal changes in node ranking. We show that the ranking dynamics follows a non-monotonous curve, suggesting an inherent partition of the nodes into qualitatively distinct stability categories. These findings provide plausible explanations to observed yet hitherto unexplained phenomena, such as how superstars fortify their ranks despite massive fluctuations in their degrees, and how stars are more prone to rank instability.
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spelling pubmed-93996912022-08-28 Beyond preferential attachment: falling of stars and survival of superstars Somin, Shahar Altshuler, Yaniv ‘Sandy’ Pentland, Alex Shmueli, Erez R Soc Open Sci Mathematics Numerous studies over the past decades established that real-world networks typically follow preferential attachment and detachment principles. Subsequently, this implies that degree fluctuations monotonically increase while rising up the ‘degree ladder’, causing high-degree nodes to be prone for attachment of new edges and for detachment of existing ones. Despite the extensive study of node degrees (absolute popularity), many domains consider node ranks (relative popularity) as of greater importance. This raises intriguing questions—what dynamics are expected to emerge when observing the ranking of network nodes over time? Does the ranking of nodes present similar monotonous patterns to the dynamics of their corresponding degrees? In this paper, we show that surprisingly the answer is not straightforward. By performing both theoretical and empirical analyses, we demonstrate that preferential principles do not apply to the temporal changes in node ranking. We show that the ranking dynamics follows a non-monotonous curve, suggesting an inherent partition of the nodes into qualitatively distinct stability categories. These findings provide plausible explanations to observed yet hitherto unexplained phenomena, such as how superstars fortify their ranks despite massive fluctuations in their degrees, and how stars are more prone to rank instability. The Royal Society 2022-08-24 /pmc/articles/PMC9399691/ /pubmed/36039282 http://dx.doi.org/10.1098/rsos.220899 Text en © 2022 The Authors. https://creativecommons.org/licenses/by/4.0/Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, provided the original author and source are credited.
spellingShingle Mathematics
Somin, Shahar
Altshuler, Yaniv
‘Sandy’ Pentland, Alex
Shmueli, Erez
Beyond preferential attachment: falling of stars and survival of superstars
title Beyond preferential attachment: falling of stars and survival of superstars
title_full Beyond preferential attachment: falling of stars and survival of superstars
title_fullStr Beyond preferential attachment: falling of stars and survival of superstars
title_full_unstemmed Beyond preferential attachment: falling of stars and survival of superstars
title_short Beyond preferential attachment: falling of stars and survival of superstars
title_sort beyond preferential attachment: falling of stars and survival of superstars
topic Mathematics
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9399691/
https://www.ncbi.nlm.nih.gov/pubmed/36039282
http://dx.doi.org/10.1098/rsos.220899
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