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Christian Tallberg
Abstract
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.