The widespread interest in quantum computation has motivated (among others) applications to network analysis, where quantum advantage may turn out to be especially beneficial for the treatment of large-scale problems. In the past years, several authors have proposed the use of quantum walks - as opposed to classical random walks - in the definition and analysis of centrality measures for graphs, which in turn are the basis for ranking algorithms. Here we focus on unitary continuous-time quantum walks (CTQW) applied to directed graphs and propose new quantum algorithms for hub and authority ranking of the nodes. In particular we explore - the choice of Hamiltonian operator that defines the time evolution of a CTQW, - the choice of the initial state of the system (which turns out to have a non-negligible effect on the final ranking), and perform numerical comparisons with well-known classical ranking algorithms such as HITS and PageRank.