  The roles of different nodes within a network are often understood through
centrality analysis, which aims to quantify the capacity of a node to
influence, or be influenced by, other nodes via its connection topology. Many
different centrality measures have been proposed, but the degree to which they
offer unique information, and such whether it is advantageous to use multiple
centrality measures to define node roles, is unclear. Here we calculate
correlations between 17 different centrality measures across 212 diverse
real-world networks, examine how these correlations relate to variations in
network density and global topology, and investigate whether nodes can be
clustered into distinct classes according to their centrality profiles. We find
that centrality measures are generally positively correlated to each other, the
strength of these correlations varies across networks, and network modularity
plays a key role in driving these cross-network variations. Data-driven
clustering of nodes based on centrality profiles can distinguish different
roles, including topological cores of highly central nodes and peripheries of
less central nodes. Our findings illustrate how network topology shapes the
pattern of correlations between centrality measures and demonstrate how a
comparative approach to network centrality can inform the interpretation of
nodal roles in complex networks.
