# Beyond Node Embedding: A Direct Unsupervised Edge Representation Framework for Homogeneous Networks

arXiv: https://arxiv.org/abs/1912.05140 · HTML: https://mlsanity.com/paper/1912.05140/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Dec 2019.

## Built on by (most cited first, 4 of 4)

- [Direct Embedding of Temporal Network Edges via Time-Decayed Line Graphs](https://mlsanity.com/paper/2210.00032/) (2022)
- [Robust vertebra identification using simultaneous node and edge predicting Graph Neural Networks](https://mlsanity.com/paper/2308.02509/) (2023)
- [Monolith to Microservices: Representing Application Software through Heterogeneous Graph Neural Network](https://mlsanity.com/paper/2112.01317/) (2021)
- [Predicting Protein-Ligand Binding Affinity with Equivariant Line Graph Network](https://mlsanity.com/paper/2210.16098/) (2022)

## Abstract (arXiv)

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.