Comparing Degree-based and Closeness-based Centrality Measures

Christian Tallberg


Statistical properties of four centrality measures are investigated. Three of the measures are extensively used within the context of social networks. The measures are investigated for two centrality concepts, degree centrality and closeness centrality. The model assumed to generate realizations of social networks is a conditional Bernoulli model where the edge probabilities are independently beta distributed. For various shape parameter values of the beta distribution, properties of the graph centrality measures are compared for degree-based centrality and closeness-based centrality.
Three of the graph centrality measures exhibit similar behaviour when they are degree-based and closeness-based. The fourth measure, the variance of the actor centralities, generate diverging tendencies of the properties of the measure depending on whether it is degree-based or closeness-based. This is interpreted as an indication that the measure captures different features of the structures of the social network when it is degree-based and closeness-based.
Keywords: Degree centrality, Closeness centrality, Bernoulli model, Beta distribution\newpage
The author would like to thank Ove Frank for helpful comments. Partial financial support from the Swedish Council of Research in Humanities and Social Sciences (HSFR), grant No. F0750/96, is gratefully acknowledged.

Close this Window