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.
- Received 25 June 2011
DOI:https://doi.org/10.1103/PhysRevLett.107.178701
© 2011 American Physical Society
Viewpoint
Few and Far Between
Published 17 October 2011
How nodes connect to each other may explain why we don’t see certain classes of networks.
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