Encyclopedia of Social Network Analysis and Mining

2014 Edition
| Editors: Reda Alhajj, Jon Rokne

Scale-Free Nature of Social Networks

  • Piotr Fronczak
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-6170-8_248
  • 78 Downloads

Synonyms

Glossary

Degree

The degree of a node in a network is the number of edges or connections to that node

Node Degree Distribution

The distribution function P(.k) that gives the probability that a node selected at random has exactlyk edges

Power-Law Distribution

Has a probability function of the form P.(x)~ xa

Fat-Tailed Distributions

Have tails that decay more slowly than exponentially. All power-law distributions are fat tailed, but not all fat-tailed distributions are power laws (e.g., the log-normal distribution is fat tailed but is not a power-law distribution)

SF Network

The network with power-law distribution of node degrees

ER Graph

The network model in which edges are set between nodes with equal probabilities

Scale-Freeness

Feature of objects or laws that does not change if length scale is multiplied by a common factor, also known as scale invariance

Definition

The notion of scale-freeness and...

This is a preview of subscription content, log in to check access.

References

  1. Aiello W, Chung F, Lu L (2002) Random evolution of massive graphs. In: Pardalos PM, Abello J, Resende MGC (eds) Handbook of massive data sets. Kluwer Academic, Dordrecht/London, pp 97–122Google Scholar
  2. Albert R, Jeong H, Barabasi A-L (1999) Diameter of the World Wide Web. Nature 401:130–131Google Scholar
  3. Aleksiejuk A, Holyst JA, Stauffer D (2002) Ferromagnetic phase transition in Barabasi-Albert networks. Physica A 310:260–266zbMATHGoogle Scholar
  4. Bak P (1996) How nature works: the science of self-organized criticality. Copernicus, New YorkzbMATHGoogle Scholar
  5. Barabasi A-L (2002) Linked: the new science of networks. Perseus Books Group, CambridgeGoogle Scholar
  6. Barabasi A-L, Albert R (1999) Emergence of scaling in random networks. Science 286:509–512MathSciNetGoogle Scholar
  7. Cohen R, Erez K, ben Avraham D, Havlin S (2000) Resilience of the Internet to random breakdowns. Phys Rev Lett 85:4626Google Scholar
  8. Cohen R, Erez K, ben Avraham D, Havlin S (2001) Breakdown of the Internet under intentional attack. Phys Rev Lett 86:3682Google Scholar
  9. de Solla Price DJ (1965) Networks of scientific papers. Science 149:510–515Google Scholar
  10. Ebel H, Mielsch LI, Bornholdt S (2002) Scale-free topology of e-mail networks. Phys Rev E 66:035103Google Scholar
  11. Erdos P, Renyi A (1960) On the evolution of random graphs. Publ Math Inst Hung Acad Sci 5: 17–61MathSciNetGoogle Scholar
  12. Goh K-I, Kahng B, Kim D (2001) Universal behaviour of load distribution in scale-free networks. Phys Rev Lett 87:278701Google Scholar
  13. Guimerà R, Mossa S, Turtschi A, Amaral LAN (2005) The worldwide air transportation network: anomalous centrality, community structure, and cities' global roles. Proc Natl Acad Sci 102:7794–7799zbMATHGoogle Scholar
  14. Liljeros F, Edling CR, Amaral LAN, Stanley HE, Aberg Y (2001) The web of human sexual contacts. Nature 411:907–908Google Scholar
  15. Newman ME, Watts DJ, Strogatz SH (2002) Random graph models of social networks. Proc Natl Acad Sci USA 99(Suppl 1):2566–2572Google Scholar
  16. Park J, Newman MEJ (2004) Statistical mechanics of networks. Phys Rev E 70:066117MathSciNetGoogle Scholar
  17. Pastor-Satorras R, Vespignani A (2001) Epidemic spreading in scale-free networks. Phys Rev Lett 86: 3200Google Scholar
  18. Pastor-Satorras R, Vespignani A (2002) Immunization of complex networks. Phys Rev E 65:036104Google Scholar
  19. Redner S (1998) How popular is your paper? An empirical study of the citation distribution. Eur Phys J B 4: 131–134Google Scholar
  20. Valverde S, Ferrer Cancho R, Solé RV (2002) Scale-free networks from optimal design. Europhys Lett 60:512Google Scholar
  21. Yeomans JM (2002) Statistical mechanics of phase transitions. Oxford University Press, New YorkGoogle Scholar
  22. Yule UG (1925) A mathematical theory of evolution, based on the conclusions of Dr. J. C. Willis, F.R.S. Philos Trans R Soc Lond B Contain Pap Biol Character 213:21–87Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Piotr Fronczak
    • 1
  1. 1.Faculty of PhysicsWarsaw University of TechnologyWarsawPoland