  We introduce a ranking model for temporal multi-dimensional weighted and
directed networks based on the Perron eigenvector of a multi-homogeneous
order-preserving map. The model extends to the temporal multilayer setting the
HITS algorithm and defines five centrality vectors: two for the nodes, two for
the layers, and one for the temporal stamps. Nonlinearity is introduced in the
standard HITS model in order to guarantee existence and uniqueness of these
centrality vectors for any network, without any requirement on its connectivity
structure. We introduce a globally convergent power iteration like algorithm
for the computation of the centrality vectors. Numerical experiments on
real-world networks are performed in order to assess the effectiveness of the
proposed model and showcase the performance of the accompanying algorithm.
