Explicit size distributions of failure cascades redefine systemic risk on finite networks

Abstract How big is the risk that a few initial failures of nodes in a network amplify to large cascades that span a substantial share of all nodes? Predicting the final cascade size is critical to ensure the functioning of a system as a whole. Yet, this task is hampered by uncertain and missing inf...

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Autores principales:	Rebekka Burkholz, Hans J. Herrmann, Frank Schweitzer
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2018
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/9c4da604ba06445e9c904b4ac1f9aecd
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spelling	oai:doaj.org-article:9c4da604ba06445e9c904b4ac1f9aecd2021-12-02T16:08:04ZExplicit size distributions of failure cascades redefine systemic risk on finite networks10.1038/s41598-018-25211-32045-2322https://doaj.org/article/9c4da604ba06445e9c904b4ac1f9aecd2018-05-01T00:00:00Zhttps://doi.org/10.1038/s41598-018-25211-3https://doaj.org/toc/2045-2322Abstract How big is the risk that a few initial failures of nodes in a network amplify to large cascades that span a substantial share of all nodes? Predicting the final cascade size is critical to ensure the functioning of a system as a whole. Yet, this task is hampered by uncertain and missing information. In infinitely large networks, the average cascade size can often be estimated by approaches building on local tree and mean field approximations. Yet, as we demonstrate, in finite networks, this average does not need to be a likely outcome. Instead, we find broad and even bimodal cascade size distributions. This phenomenon persists for system sizes up to 107 and different cascade models, i.e. it is relevant for most real systems. To show this, we derive explicit closed-form solutions for the full probability distribution of the final cascade size. We focus on two topological limit cases, the complete network representing a dense network with a very narrow degree distribution, and the star network representing a sparse network with a inhomogeneous degree distribution. Those topologies are of great interest, as they either minimize or maximize the average cascade size and are common motifs in many real world networks.Rebekka BurkholzHans J. HerrmannFrank SchweitzerNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 8, Iss 1, Pp 1-8 (2018)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Rebekka Burkholz Hans J. Herrmann Frank Schweitzer Explicit size distributions of failure cascades redefine systemic risk on finite networks
description	Abstract How big is the risk that a few initial failures of nodes in a network amplify to large cascades that span a substantial share of all nodes? Predicting the final cascade size is critical to ensure the functioning of a system as a whole. Yet, this task is hampered by uncertain and missing information. In infinitely large networks, the average cascade size can often be estimated by approaches building on local tree and mean field approximations. Yet, as we demonstrate, in finite networks, this average does not need to be a likely outcome. Instead, we find broad and even bimodal cascade size distributions. This phenomenon persists for system sizes up to 107 and different cascade models, i.e. it is relevant for most real systems. To show this, we derive explicit closed-form solutions for the full probability distribution of the final cascade size. We focus on two topological limit cases, the complete network representing a dense network with a very narrow degree distribution, and the star network representing a sparse network with a inhomogeneous degree distribution. Those topologies are of great interest, as they either minimize or maximize the average cascade size and are common motifs in many real world networks.
format	article
author	Rebekka Burkholz Hans J. Herrmann Frank Schweitzer
author_facet	Rebekka Burkholz Hans J. Herrmann Frank Schweitzer
author_sort	Rebekka Burkholz
title	Explicit size distributions of failure cascades redefine systemic risk on finite networks
title_short	Explicit size distributions of failure cascades redefine systemic risk on finite networks
title_full	Explicit size distributions of failure cascades redefine systemic risk on finite networks
title_fullStr	Explicit size distributions of failure cascades redefine systemic risk on finite networks
title_full_unstemmed	Explicit size distributions of failure cascades redefine systemic risk on finite networks
title_sort	explicit size distributions of failure cascades redefine systemic risk on finite networks
publisher	Nature Portfolio
publishDate	2018
url	https://doaj.org/article/9c4da604ba06445e9c904b4ac1f9aecd
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_version_	1718384674432090112

Explicit size distributions of failure cascades redefine systemic risk on finite networks

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