All scale-free networks are sparse
Physics and Society
2011-11-04 v2 Statistical Mechanics
Social and Information Networks
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.
Keywords
Cite
@article{arxiv.1106.5150,
title = {All scale-free networks are sparse},
author = {Charo I. Del Genio and Thilo Gross and Kevin E. Bassler},
journal= {arXiv preprint arXiv:1106.5150},
year = {2011}
}
Comments
4 pages, 2 figures