Advertisement

Correlation Coefficient Analysis of Centrality Metrics for Complex Network Graphs

  • Natarajan MeghanathanEmail author
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 348)

Abstract

The high-level contribution of this paper is a correlation coefficient analysis of the well-known centrality metrics (degree centrality, eigenvector centrality, betweenness centrality, closeness centrality, farness centrality and eccentricity) for network analysis studies on real-world network graphs representing diverse domains (ranging from 34 nodes to 332 nodes). We observe the two degree-based centrality metrics (degree and eigenvector centrality) to be highly correlated across all the networks studied. There is predominantly a moderate level of correlation between any two of the shortest paths-based centrality metrics (betweenness, closeness, farness and eccentricity) and such a correlation is consistently observed across all the networks. Though we observe a poor correlation between a degree-based centrality metric and a shortest-path based centrality metric for regular random networks, as the variation in the degree distribution of the vertices increases (i.e., as the network gets increasingly scale-free), the correlation coefficient between the two classes of centrality metrics increases.

Keywords

Centrality Complex Networks Correlation Coefficient Degree Shortest Paths 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Newman, M.: Networks: An Introduction. Oxford University Press, Oxford (2010)CrossRefGoogle Scholar
  2. 2.
  3. 3.
  4. 4.
    Li, C., Li, Q., Van Mieghem, P., Stanley, H.E., Wang, H.: Correlation between Centrality Metrics and their Application to the Opinion Model. arXiv:1409.6033v1 (2014)Google Scholar
  5. 5.
    Strang, G.: Linear Algebra and its Applications. Cengage Learning, Boston (2005)Google Scholar
  6. 6.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms. MIT Press, Cambridge (2009)zbMATHGoogle Scholar
  7. 7.
    Zachary, W.W.: An Information Flow Model for Conflict and Fission in Small Groups. Journal of Anthropological Research 33, 452–473 (1977)Google Scholar
  8. 8.
    Lusseau, D., Schneider, K., Boisseau, O.J., Haase, P., Slooten, E., Dawson, S.M.: The Bottlenose Dolphin Community of Doubtful Sound Features a Large Proportion of Long Lasting Associations. Behavioral Ecology and Sociobiology 54, 396–405 (2003)CrossRefGoogle Scholar
  9. 9.
  10. 10.
    Newman, M.E.J.: Finding Community Structure in Networks using the Eigenvectors of Matrices. Physics Review. E 74, 36104 (2006)CrossRefGoogle Scholar
  11. 11.
    Clauset, A., Newman, M.E.J., Moore, C.: Finding Community Structure in Very Large Networks. Physics Review. E 70, 066111 (2004)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Jackson State UniversityJacksonUSA

Personalised recommendations