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  All Scale-Free Networks Are Sparse

Del Genio, C. I., Gross, T., & Bassler, K. E. (2011). All Scale-Free Networks Are Sparse. Physical Review Letters, 107(17): 178701.

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Del Genio, C. I.1, Author           
Gross, T.1, Author           
Bassler, K. E.1, Author           
Affiliations:
1Max Planck Institute for the Physics of Complex Systems, Max Planck Society, ou_2117288              

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 MPIPKS: YB 2012
 Abstract: We study the realizability of scale-free networks with a given degree sequence, showing that the fraction of realizable sequences undergoes two first-order transitions at the values 0 and 2 of the power-law exponent. We substantiate this finding by analytical reasoning and by a numerical method, proposed here, based on extreme value arguments, which can be applied to any given degree distribution. Our results reveal a fundamental reason why large scale-free networks without constraints on minimum and maximum degree must be sparse.

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 Dates: 2011-10-17
 Publication Status: Issued
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 Identifiers: eDoc: 608142
ISI: 000296373600038
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Title: Physical Review Letters
Source Genre: Journal
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Pages: - Volume / Issue: 107 (17) Sequence Number: 178701 Start / End Page: - Identifier: ISSN: 0031-9007