  Hierarchy and centrality are two popular notions used to characterize the
importance of entities in complex systems. Indeed, many complex systems exhibit
a natural hierarchical structure, and centrality is a fundamental
characteristic allowing to identify key constituents. Several measures based on
various aspects of network topology have been proposed in order to quantify
these concepts. While numerous studies have investigated whether centrality
measures convey redundant information, how centrality and hierarchy measures
are related is still an open issue. In this paper, we investigate the
interaction between centrality and hierarchy using several correlation and
similarity evaluation measures. A series of experiments is performed in order
to evaluate the combinations of 6 centrality measures with 4 hierarchy measures
across 28 diverse real-world networks with varying topological characteristics.
Results show that network density and transitivity play a key role in shaping
the pattern of relations between centrality and hierarchy measures.
