# Direct Embedding of Temporal Network Edges via Time-Decayed Line Graphs

arXiv: https://arxiv.org/abs/2210.00032 · HTML: https://mlsanity.com/paper/2210.00032/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 56 references that are in the map.
- First posted on arXiv 30 Sep 2022.

## Builds on (most cited first, 26 of 26)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Embedding Entities and Relations for Learning and Inference in Knowledge Bases](https://mlsanity.com/paper/1412.6575/) (2014)
- [LINE: Large-scale Information Network Embedding](https://mlsanity.com/paper/1503.03578/) (2015)
- [Temporal Graph Networks for Deep Learning on Dynamic Graphs](https://mlsanity.com/paper/2006.10637/) (2020)
- [Inductive Representation Learning on Temporal Graphs](https://mlsanity.com/paper/2002.07962/) (2020)
- [EvolveGCN: Evolving Graph Convolutional Networks for Dynamic Graphs](https://mlsanity.com/paper/1902.10191/) (2019)
- [Structured Sequence Modeling with Graph Convolutional Recurrent Networks](https://mlsanity.com/paper/1612.07659/) (2016)
- [Network Embedding as Matrix Factorization: Unifying DeepWalk, LINE, PTE, and node2vec](https://mlsanity.com/paper/1710.02971/) (2017)
- [Know-Evolve: Deep Temporal Reasoning for Dynamic Knowledge Graphs](https://mlsanity.com/paper/1705.05742/) (2017)
- [DynGEM: Deep Embedding Method for Dynamic Graphs](https://mlsanity.com/paper/1805.11273/) (2018)
- [dyngraph2vec: Capturing Network Dynamics using Dynamic Graph Representation Learning](https://mlsanity.com/paper/1809.02657/) (2018)
- [Variational Graph Recurrent Neural Networks](https://mlsanity.com/paper/1908.09710/) (2019)
- [SNAP: A General Purpose Network Analysis and Graph Mining Library](https://mlsanity.com/paper/1606.07550/) (2016)
- [Provably expressive temporal graph networks](https://mlsanity.com/paper/2209.15059/) (2022)
- [Attributed Network Embedding for Learning in a Dynamic Environment](https://mlsanity.com/paper/1706.01860/) (2017)
- [TIMERS: Error-Bounded SVD Restart on Dynamic Networks](https://mlsanity.com/paper/1711.09541/) (2017)
- [Dual-Primal Graph Convolutional Networks](https://mlsanity.com/paper/1806.00770/) (2018)
- [Easing Embedding Learning by Comprehensive Transcription of Heterogeneous Information Networks](https://mlsanity.com/paper/1807.03490/) (2018)
- [K-Core based Temporal Graph Convolutional Network for Dynamic Graphs](https://mlsanity.com/paper/2003.09902/) (2020)
- [DyLink2Vec: Effective Feature Representation for Link Prediction in Dynamic Networks](https://mlsanity.com/paper/1804.05755/) (2018)
- [The Block Point Process Model for Continuous-Time Event-Based Dynamic Networks](https://mlsanity.com/paper/1711.10967/) (2017)
- [Beyond Node Embedding: A Direct Unsupervised Edge Representation Framework for Homogeneous Networks](https://mlsanity.com/paper/1912.05140/) (2019)

## Built on by (most cited first, 5 of 5)

- [Temporal Graph Benchmark for Machine Learning on Temporal Graphs](https://mlsanity.com/paper/2307.01026/) (2023)
- [Universal Time-Series Representation Learning: A Survey](https://mlsanity.com/paper/2401.03717/) (2024)
- [CAT-Walk: Inductive Hypergraph Learning via Set Walks](https://mlsanity.com/paper/2306.11147/) (2023)
- [ScaDyG:A New Paradigm for Large-scale Dynamic Graph Learning](https://mlsanity.com/paper/2501.16002/) (2025)
- [Graph Memory: A Structured and Interpretable Framework for Modality-Agnostic Embedding-Based Inference](https://mlsanity.com/paper/2511.14961/) (2025)

## Abstract (arXiv)

Temporal networks model a variety of important phenomena involving timed interactions between entities. Existing methods for machine learning on temporal networks generally exhibit at least one of two limitations. First, time is assumed to be discretized, so if the time data is continuous, the user must determine the discretization and discard precise time information. Second, edge representations can only be calculated indirectly from the nodes, which may be suboptimal for tasks like edge classification. We present a simple method that avoids both shortcomings: construct the line graph of the network, which includes a node for each interaction, and weigh the edges of this graph based on the difference in time between interactions. From this derived graph, edge representations for the original network can be computed with efficient classical methods. The simplicity of this approach facilitates explicit theoretical analysis: we can constructively show the effectiveness of our method's representations for a natural synthetic model of temporal networks. Empirical results on real-world networks demonstrate our method's efficacy and efficiency on both edge classification and temporal link prediction.