  Using each node's degree as a proxy for its importance, the topological
hierarchy of a complex network is introduced and quantified. We propose a
simple dynamical process used to construct networks which are either maximally
or minimally hierarchical. Comparison with these extremal cases as well as with
random scale-free networks allows us to better understand hierarchical versus
modular features in several real-life complex networks. For random scale-free
topologies the extent of topological hierarchy is shown to smoothly decline
with $\gamma$ -- the exponent of a degree distribution -- reaching its highest
possible value for $\gamma \leq 2$ and quickly approaching zero for $\gamma>3$.
