  Identifying vital nodes in networks exhibiting a community structure is a
fundamental issue. Indeed, community structure is one of the main properties of
real-world networks. Recent works have shown that community-aware centrality
measures compare favorably with classical measures agnostic about this
ubiquitous property. Nonetheless, there is no clear consensus about how they
relate and in which situation it is better to use a classical or a
community-aware centrality measure. To this end, in this paper, we perform an
extensive investigation to get a better understanding of the relationship
between classical and community-aware centrality measures reported in the
literature. Experiments use artificial networks with controlled community
structure properties and a large sample of real-world networks originating from
various domains. Results indicate that the stronger the community structure,
the more appropriate the community-aware centrality measures. Furthermore,
variations of the degree and community size distribution parameters do not
affect the results. Finally, network transitivity and community structure
strength are the most significant drivers controlling the interactions between
classical and community-aware centrality measures.
