  Multilayer network analysis is a useful approach for studying the structural
properties of entities with diverse, multitudinous relations. Classifying the
importance of nodes and node-layer tuples is an important aspect of the study
of multilayer networks. To do this, it is common to calculate various
centrality measures, which allow one to rank nodes and node-layers according to
a variety of structural features. In this paper, we formulate occupation,
PageRank, betweenness, and closeness centralities in terms of node-occupation
properties of different types of continuous-time classical and quantum random
walks on multilayer networks. We apply our framework to a variety of synthetic
and real-world multilayer networks, and we identify marked differences between
classical and quantum centrality measures. Our computations also give insights
into the correlations between certain random-walk-based and geodesic-path-based
centralities.
