  Graph neural networks have recently achieved remarkable success in
representing graph-structured data, with rapid progress in both the node
embedding and graph pooling methods. Yet, they mostly focus on capturing
information from the nodes considering their connectivity, and not much work
has been done in representing the edges, which are essential components of a
graph. However, for tasks such as graph reconstruction and generation, as well
as graph classification tasks for which the edges are important for
discrimination, accurately representing edges of a given graph is crucial to
the success of the graph representation learning. To this end, we propose a
novel edge representation learning framework based on Dual Hypergraph
Transformation (DHT), which transforms the edges of a graph into the nodes of a
hypergraph. This dual hypergraph construction allows us to apply
message-passing techniques for node representations to edges. After obtaining
edge representations from the hypergraphs, we then cluster or drop edges to
obtain holistic graph-level edge representations. We validate our edge
representation learning method with hypergraphs on diverse graph datasets for
graph representation and generation performance, on which our method largely
outperforms existing graph representation learning methods. Moreover, our edge
representation learning and pooling method also largely outperforms
state-of-the-art graph pooling methods on graph classification, not only
because of its accurate edge representation learning, but also due to its
lossless compression of the nodes and removal of irrelevant edges for effective
message-passing.
