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.
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References
Newman, M.: Networks: An Introduction. Oxford University Press, Oxford (2010)
Gephi, http://gephi.github.io/
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)
Strang, G.: Linear Algebra and its Applications. Cengage Learning, Boston (2005)
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms. MIT Press, Cambridge (2009)
Zachary, W.W.: An Information Flow Model for Conflict and Fission in Small Groups. Journal of Anthropological Research 33, 452–473 (1977)
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)
Orgnet.com, http://www.orgnet.com/divided.html
Newman, M.E.J.: Finding Community Structure in Networks using the Eigenvectors of Matrices. Physics Review. E 74, 36104 (2006)
Clauset, A., Newman, M.E.J., Moore, C.: Finding Community Structure in Very Large Networks. Physics Review. E 70, 066111 (2004)
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© 2015 Springer International Publishing Switzerland
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Meghanathan, N. (2015). Correlation Coefficient Analysis of Centrality Metrics for Complex Network Graphs. In: Silhavy, R., Senkerik, R., Oplatkova, Z., Prokopova, Z., Silhavy, P. (eds) Intelligent Systems in Cybernetics and Automation Theory. CSOC 2015. Advances in Intelligent Systems and Computing, vol 348. Springer, Cham. https://doi.org/10.1007/978-3-319-18503-3_2
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DOI: https://doi.org/10.1007/978-3-319-18503-3_2
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-18502-6
Online ISBN: 978-3-319-18503-3
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