%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 }