All scale-free networks are sparse

Charo del Genio, Thilo Gross, Kevin Bassler

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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.
Original languageEnglish
Article number178701
JournalPhysical Review Letters
Volume107
DOIs
Publication statusPublished - 17 Oct 2011

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Copyright © and Moral Rights are retained by the author(s) and/ or other copyright owners. A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. This item cannot be reproduced or quoted extensively from without first obtaining permission in writing from the copyright holder(s). The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the copyright holders.

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All scale-free networks are sparse. / del Genio, Charo; Gross, Thilo; Bassler, Kevin.

In: Physical Review Letters, Vol. 107, 178701, 17.10.2011.

Research output: Contribution to journalArticle

del Genio, Charo ; Gross, Thilo ; Bassler, Kevin. / All scale-free networks are sparse. In: Physical Review Letters. 2011 ; Vol. 107.
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