  Graph embedding is becoming an important method with applications in various
areas, including social networks and knowledge graph completion. In particular,
Poincar\'e embedding has been proposed to capture the hierarchical structure of
graphs, and its effectiveness has been reported. However, most of the existing
methods have isometric mappings in the embedding space, and the choice of the
origin point can be arbitrary. This fact is not desirable when the distance
from the origin is used as an indicator of hierarchy, as in the case of
Poincar\'e embedding. In this paper, we propose graph embedding in a metric
cone to solve such a problem, and we gain further benefits: 1) we provide an
indicator of hierarchical information that is both geometrically and
intuitively natural to interpret, 2) we can extract the hierarchical structure
from a graph embedding output of other methods by learning additional
one-dimensional parameters, and 3) we can change the curvature of the embedding
space via a hyperparameter.
