  Graph embedding methods embed the nodes in a graph in low dimensional vector
space while preserving graph topology to carry out the downstream tasks such as
link prediction, node recommendation and clustering. These tasks depend on a
similarity measure such as cosine similarity and Euclidean distance between a
pair of embeddings that are symmetric in nature and hence do not hold good for
directed graphs. Recent work on directed graphs, HOPE, APP, and NERD, proposed
to preserve the direction of edges among nodes by learning two embeddings,
source and target, for every node. However, these methods do not take into
account the properties of directed edges explicitly. To understand the
directional relation among nodes, we propose a novel approach that takes
advantage of the non commutative property of vector cross product to learn
embeddings that inherently preserve the direction of edges among nodes. We
learn the node embeddings through a Siamese neural network where the
cross-product operation is incorporated into the network architecture. Although
cross product between a pair of vectors is defined in three dimensional, the
approach is extended to learn N dimensional embeddings while maintaining the
non-commutative property. In our empirical experiments on three real-world
datasets, we observed that even very low dimensional embeddings could
effectively preserve the directional property while outperforming some of the
state-of-the-art methods on link prediction and node recommendation tasks
