Random processes with high variance produce scale free networks.
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| Title: | Random processes with high variance produce scale free networks. |
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| Authors: | Johnston, Josh1 (AUTHOR) jjohnston@u.boisestate.edu, Andersen, Tim1 (AUTHOR) tandersen@boisestate.edu |
| Source: | Physica A. Oct2022, Vol. 604, pN.PAG-N.PAG. 1p. |
| Subjects: | Central limit theorem, Geometric distribution, Random graphs |
| Abstract: | Real-world networks tend to be scale free, having heavy-tailed degree distributions with more hubs than predicted by classical random graph generation methods. Preferential attachment and growth are the most commonly accepted mechanisms leading to these networks and are incorporated in the Barabási–Albert (BA) model (Barabási, 2009 [1]). We provide an alternative model using a randomly stopped linking process inspired by a generalized Central Limit Theorem (CLT) for geometric distributions with widely varying parameters. The common characteristic of both the BA model and our randomly stopped linking model is the mixture of widely varying geometric distributions, suggesting the critical characteristic of scale free networks is high variance, not growth or preferential attachment. The limitation of classical random graph models is low variance in parameters, while scale free networks are the natural, expected result of real-world variance. • Randomly stopped linking model generates scale free networks. • Scale free networks expected from any Bernoulli process with high variance. • Preferential attachment and growth not needed for scale free networks. • Heavy-tailed degree distributions come from mixture of geometric distributions. [ABSTRACT FROM AUTHOR] |
| Copyright of Physica A is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 158745175 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Random processes with high variance produce scale free networks. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Johnston%2C+Josh%22">Johnston, Josh</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> jjohnston@u.boisestate.edu</i><br /><searchLink fieldCode="AR" term="%22Andersen%2C+Tim%22">Andersen, Tim</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> tandersen@boisestate.edu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Physica+A%22">Physica A</searchLink>. Oct2022, Vol. 604, pN.PAG-N.PAG. 1p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Central+limit+theorem%22">Central limit theorem</searchLink><br /><searchLink fieldCode="DE" term="%22Geometric+distribution%22">Geometric distribution</searchLink><br /><searchLink fieldCode="DE" term="%22Random+graphs%22">Random graphs</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Real-world networks tend to be scale free, having heavy-tailed degree distributions with more hubs than predicted by classical random graph generation methods. Preferential attachment and growth are the most commonly accepted mechanisms leading to these networks and are incorporated in the Barabási–Albert (BA) model (Barabási, 2009 [1]). We provide an alternative model using a randomly stopped linking process inspired by a generalized Central Limit Theorem (CLT) for geometric distributions with widely varying parameters. The common characteristic of both the BA model and our randomly stopped linking model is the mixture of widely varying geometric distributions, suggesting the critical characteristic of scale free networks is high variance, not growth or preferential attachment. The limitation of classical random graph models is low variance in parameters, while scale free networks are the natural, expected result of real-world variance. • Randomly stopped linking model generates scale free networks. • Scale free networks expected from any Bernoulli process with high variance. • Preferential attachment and growth not needed for scale free networks. • Heavy-tailed degree distributions come from mixture of geometric distributions. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Physica A is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.physa.2022.127588 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 1 StartPage: N.PAG Subjects: – SubjectFull: Central limit theorem Type: general – SubjectFull: Geometric distribution Type: general – SubjectFull: Random graphs Type: general Titles: – TitleFull: Random processes with high variance produce scale free networks. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Johnston, Josh – PersonEntity: Name: NameFull: Andersen, Tim IsPartOfRelationships: – BibEntity: Dates: – D: 15 M: 10 Text: Oct2022 Type: published Y: 2022 Identifiers: – Type: issn-print Value: 03784371 Numbering: – Type: volume Value: 604 Titles: – TitleFull: Physica A Type: main |
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