On the betweenness centrality of trees, forests and cycles

Thomas Britz

Article ID: 968
Vol 2, Issue 2, 2019

VIEWS - 8199 (Abstract)

Abstract


Simple mathematical expressions are given for the betweenness centrality of nodes in trees, forests and cycles. As application, a centrality test is given for when a network might be a forest.


Keywords


Tree; Forest; Cycle; Network; Betweenness Centrality; Connected Component

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References

  1. O. Abramov, Network Theory Applied to Linguistics - New Advances in Language Classification and Typology, PhD thesis, Bielefeld University, 2011.
  2. R. Aris, "Prolegomena to the rational analysis of systems of chemical reactions," Archive for Rational Mechanics and Analysis, vol. 19, pp. 81-99, 1965.
  3. D. Bright, C. Greenhill, T. Britz, A. Ritter and C. Morselli, "Criminal network vulnerabilities and adaptations," Global Crime, vol. 18, pp. 424-441, 2017.
  4. R. Diestel, Graph Theory, 2nd ed., Springer-Verlag, 1999.
  5. L. Ford, Jr. and D. Fulkerson, Flows in Networks, Princeton University Press, 1962.
  6. D. Hunter, T. Britz, M. Jones and M. Letnic, "Reintroduction of Tasmanian devils to mainland Australia can restore top-down control in ecosystems where dingoes have been extirpated," Conservation Biology, vol. 191, pp. 428-435, 2015.
  8. E. Otte and R. Rousseau, "Social network analysis: a powerful strategy, also for the information sciences," Journal of Information Science, vol. 28, pp. 441-453, 2002.
  9. B. Tran, P. Straka, M. Falster, K. Douglas, T. Britz and L. Gorm, "Overcoming the data drought: exploring general practice in Australia by network analysis of big data," Medical Journal of Australia, Vols. , to appear, 2018.
  10. L. Freeman, "A set of measures of centrality based on betweenness," Sociometry, vol. 40, pp. 35-41, 1977.


DOI: https://doi.org/10.24294/sf.v1i2.968

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