  Many real world systems can be expressed as complex networks of
interconnected nodes. It is frequently important to be able to quantify the
relative importance of the various nodes in the network, a task accomplished by
defining some centrality measures, with different centrality definitions
stressing different aspects of the network. It is interesting to know to what
extent these different centrality definitions are related for different
networks. In this work, we study the correlation between pairs of a set of
centrality measures for different real world networks and two network models.
We show that the centralities are in general correlated, but with stronger
correlations for network models than for real networks. We also show that the
strength of the correlation of each pair of centralities varies from network to
network. Taking this fact into account, we propose the use of a centrality
correlation profile, consisting of the values of the correlation coefficients
between all pairs of centralities of interest, as a way to characterize
networks. Using the yeast protein interaction network as an example we show
also that the centrality correlation profile can be used to assess the adequacy
of a network model as a representation of a given real network.
