  The inductive biases of graph representation learning algorithms are often
encoded in the background geometry of their embedding space. In this paper, we
show that general directed graphs can be effectively represented by an
embedding model that combines three components: a pseudo-Riemannian metric
structure, a non-trivial global topology, and a unique likelihood function that
explicitly incorporates a preferred direction in embedding space. We
demonstrate the representational capabilities of this method by applying it to
the task of link prediction on a series of synthetic and real directed graphs
from natural language applications and biology. In particular, we show that
low-dimensional cylindrical Minkowski and anti-de Sitter spacetimes can produce
equal or better graph representations than curved Riemannian manifolds of
higher dimensions.
