English
 
Help Privacy Policy Disclaimer
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT

Released

Journal Article

All Scale-Free Networks Are Sparse

MPS-Authors
/persons/resource/persons184445

Del Genio,  C. I.
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

/persons/resource/persons145783

Gross,  T.
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

/persons/resource/persons184337

Bassler,  K. E.
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

External Resource
No external resources are shared
Fulltext (restricted access)
There are currently no full texts shared for your IP range.
Fulltext (public)
There are no public fulltexts stored in PuRe
Supplementary Material (public)
There is no public supplementary material available
Citation

Del Genio, C. I., Gross, T., & Bassler, K. E. (2011). All Scale-Free Networks Are Sparse. Physical Review Letters, 107(17): 178701.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0029-8BF1-1
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.