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arXiv · 1106.5150

All scale-free networks are sparse

Charo I. Del Genio·Thilo Gross·Kevin E. 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.

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Charo I. Del Genio, Thilo Gross, Kevin E. Bassler. 2011-08-26. All scale-free networks are sparse. https://doi.org/10.1103/physrevlett.107.178701

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