  Complex networks are formal frameworks capturing the interdependencies
between the elements of large systems and databases. This formalism allows to
use network navigation methods to rank the importance that each constituent has
on the global organization of the system. A key example is Pagerank navigation
which is at the core of the most used search engine of the World Wide Web.
Inspired in this classical algorithm, we define a quantum navigation method
providing a unique ranking of the elements of a network. We analyze the
convergence of quantum navigation to the stationary rank of networks and show
that quantumness decreases the number of navigation steps before convergence.
In addition, we show that quantum navigation allows to solve degeneracies found
in classical ranks. By implementing the quantum algorithm in real networks, we
confirm these improvements and show that quantum coherence unveils new
hierarchical features about the global organization of complex systems.
