  Network representation learning has traditionally been used to find lower
dimensional vector representations of the nodes in a network. However, there
are very important edge driven mining tasks of interest to the classical
network analysis community, which have mostly been unexplored in the network
embedding space. For applications such as link prediction in homogeneous
networks, vector representation (i.e., embedding) of an edge is derived
heuristically just by using simple aggregations of the embeddings of the end
vertices of the edge. Clearly, this method of deriving edge embedding is
suboptimal and there is a need for a dedicated unsupervised approach for
embedding edges by leveraging edge properties of the network.
  Towards this end, we propose a novel concept of converting a network to its
weighted line graph which is ideally suited to find the embedding of edges of
the original network. We further derive a novel algorithm to embed the line
graph, by introducing the concept of collective homophily. To the best of our
knowledge, this is the first direct unsupervised approach for edge embedding in
homogeneous information networks, without relying on the node embeddings. We
validate the edge embeddings on three downstream edge mining tasks. Our
proposed optimization framework for edge embedding also generates a set of node
embeddings, which are not just the aggregation of edges. Further experimental
analysis shows the connection of our framework to the concept of node
centrality.
