  Digraph Representation Learning (DRL) aims to learn representations for
directed homogeneous graphs (digraphs). Prior work in DRL is largely
constrained (e.g., limited to directed acyclic graphs), or has poor
generalizability across tasks (e.g., evaluated solely on one task). Most Graph
Neural Networks (GNNs) exhibit poor performance on digraphs due to the neglect
of modeling neighborhoods and preserving asymmetry. In this paper, we address
these notable challenges by leveraging hyperbolic collaborative learning from
multi-ordered and partitioned neighborhoods, and regularizers inspired by
socio-psychological factors. Our resulting formalism, Digraph Hyperbolic
Networks (D-HYPR) - albeit conceptually simple - generalizes to digraphs where
cycles and non-transitive relations are common, and is applicable to multiple
downstream tasks including node classification, link presence prediction, and
link property prediction. In order to assess the effectiveness of D-HYPR,
extensive evaluations were performed across 8 real-world digraph datasets
involving 21 prior techniques. D-HYPR statistically significantly outperforms
the current state of the art. We release our code at
https://github.com/hongluzhou/dhypr
