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.
%0 Journal Article
%1 DelGenio2011
%A Del Genio, Charo I.
%A Gross, Thilo
%A Bassler, Kevin E.
%D 2011
%I American Physical Society
%J Phys. Rev. Lett.
%K critical-phenomena graphs networks phase-transition scale-free
%P 178701
%R 10.1103/PhysRevLett.107.178701
%T All Scale-Free Networks Are Sparse
%V 107
%X 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.
@article{DelGenio2011,
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.},
added-at = {2011-10-17T17:47:02.000+0200},
author = {{Del Genio}, Charo I. and Gross, Thilo and Bassler, Kevin E.},
biburl = {https://www.bibsonomy.org/bibtex/220b824203cbe6541c197e3f8a90eaf65/rincedd},
doi = {10.1103/PhysRevLett.107.178701},
file = {DelGenio2011 - All Scale-Free Networks Are Sparse.pdf:DelGenio2011 - All Scale-Free Networks Are Sparse.pdf:PDF},
groups = {public},
interhash = {b4699a39cf72af253632a8d04e0dd432},
intrahash = {468dea6cd1ac6d980792d96bf7359742},
journal = {Phys. Rev. Lett.},
keywords = {critical-phenomena graphs networks phase-transition scale-free},
pages = 178701,
publisher = {American Physical Society},
timestamp = {2011-10-17T17:51:49.000+0200},
title = {All Scale-Free Networks Are Sparse},
username = {rincedd},
volume = 107,
year = 2011
}