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All scale-free networks are sparse
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Del Genio, Charo I., Gross, Thilo and Bassler, Kevin (2011) All scale-free networks are sparse. Physical Review Letters, Vol.107 (No.17). Article no. 1 78701 . doi:10.1103/PhysRevLett.107.178701 ISSN 0031-9007.
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Official URL: http://dx.doi.org/10.1103/PhysRevLett.107.178701
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.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Journal or Publication Title: | Physical Review Letters | ||||
| Publisher: | American Physical Society | ||||
| ISSN: | 0031-9007 | ||||
| Official Date: | 2011 | ||||
| Dates: |
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| Volume: | Vol.107 | ||||
| Number: | No.17 | ||||
| Page Range: | Article no. 1 78701 | ||||
| DOI: | 10.1103/PhysRevLett.107.178701 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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