  The study of hypergraphs has received a lot of attention over the past few
years, however up until recently there has been no interest in systems where
higher order interactions are not undirected. In this article we introduce the
notion of heterogeneous hypergraphs from an algebraic point of view, which have
traditional directed hypergraphs as a particular case. We furthermore
analytically study the spectral centralities associated to some types of
heterogeneous hypergraphs, extending previously defined eigenvector-like
centrality measures to this new realm. We supplement the analytical arguments
with some numerical comparisons of pairwise and higher order rankings, and we
construct directed higher order networks from real data.
