DOI: 10.1073/pnas.0501179102. Subnets of scale-free networks are not scale-free: Sampling properties of networks

Subnets of scale-free networks are not scale-free: Sampling properties of networks

10.1073/pnas.0501179102

Crossref journal-article

Proceedings of the National Academy of Sciences

Proceedings of the National Academy of Sciences (341)

Abstract

Most studies of networks have only looked at small subsets of the true network. Here, we discuss the sampling properties of a network's degree distribution under the most parsimonious sampling scheme. Only if the degree distributions of the network and randomly sampled subnets belong to the same family of probability distributions is it possible to extrapolate from subnet data to properties of the global network. We show that this condition is indeed satisfied for some important classes of networks, notably classical random graphs and exponential random graphs. For scale-free degree distributions, however, this is not the case. Thus, inferences about the scale-free nature of a network may have to be treated with some caution. The work presented here has important implications for the analysis of molecular networks as well as for graph theory and the theory of networks in general.

Bibliography

Stumpf, M. P. H., Wiuf, C., & May, R. M. (2005). Subnets of scale-free networks are not scale-free: Sampling properties of networks. Proceedings of the National Academy of Sciences, 102(12), 4221â4224.

Authors 3

Michael P. H. Stumpf (first)
Carsten Wiuf (additional)
Robert M. May (additional)

References 16 Referenced 404

10.1126/science.286.5439.509
10.1103/RevModPhys.74.47
Newman, M. J. E. (2003) Soc. Industrial Appl. Math. Rev. 45, 167–256. / Soc. Industrial Appl. Math. Rev. (2003)
10.1103/PhysRevE.64.046118
10.1073/pnas.2235584100
10.1126/science.1065103
10.1038/sj.embor.7400090
10.1038/35036627
10.1103/PhysRevE.68.036122
10.1038/43601
10.1073/pnas.122653799
10.1073/pnas.192448799
10.1002/pmic.200300636
Bollobás B. (1998) Random Graphs (Cambridge Univ. Press Cambridge U.K.). (10.1007/978-1-4612-0619-4_7)
Jensen H. J. (1998) Self-Organized Criticality (Cambridge Univ. Press Cambridge U.K.). (10.1017/CBO9780511622717)
Kim, H. Kim, I., Lee, Y. & Kahng, B. (2002) J. Korean Phys. Soc. 40, 1105–1108. / J. Korean Phys. Soc. (2002)

Dates

Type	When
Created	20 years, 5 months ago (March 14, 2005, 10:41 p.m.)
Deposited	3 years, 4 months ago (April 12, 2022, 12:39 p.m.)
Indexed	1 week, 6 days ago (Aug. 23, 2025, 1:01 a.m.)
Issued	20 years, 5 months ago (March 14, 2005)
Published	20 years, 5 months ago (March 14, 2005)
Published Online	20 years, 5 months ago (March 14, 2005)
Published Print	20 years, 5 months ago (March 22, 2005)

Funders 0

None

BibTeX

@article{Stumpf_2005, title={Subnets of scale-free networks are not scale-free: Sampling properties of networks}, volume={102}, ISSN={1091-6490}, url={http://dx.doi.org/10.1073/pnas.0501179102}, DOI={10.1073/pnas.0501179102}, number={12}, journal={Proceedings of the National Academy of Sciences}, publisher={Proceedings of the National Academy of Sciences}, author={Stumpf, Michael P. H. and Wiuf, Carsten and May, Robert M.}, year={2005}, month=mar, pages={4221–4224} }

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