# Exploring the Representational Power of Graph Autoencoder

arXiv: https://arxiv.org/abs/2106.12005 · HTML: https://mlsanity.com/paper/2106.12005/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 32 references that are in the map.
- First posted on arXiv 22 Jun 2021.

## Builds on (most cited first, 22 of 22)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Instance Normalization: The Missing Ingredient for Fast Stylization](https://mlsanity.com/paper/1607.08022/) (2016)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Representation Learning on Graphs: Methods and Applications](https://mlsanity.com/paper/1709.05584/) (2017)
- [A Comprehensive Survey of Graph Embedding: Problems, Techniques and Applications](https://mlsanity.com/paper/1709.07604/) (2017)
- [Deep Graph Library: A Graph-Centric, Highly-Performant Package for Graph Neural Networks](https://mlsanity.com/paper/1909.01315/) (2019)
- [Graph Embedding Techniques, Applications, and Performance: A Survey](https://mlsanity.com/paper/1705.02801/) (2017)
- [Attributed Graph Clustering: A Deep Attentional Embedding Approach](https://mlsanity.com/paper/1906.06532/) (2019)
- [DeepInf: Social Influence Prediction with Deep Learning](https://mlsanity.com/paper/1807.05560/) (2018)
- [Efficient Parameter-free Clustering Using First Neighbor Relations](https://mlsanity.com/paper/1902.11266/) (2019)
- [DEMO-Net: Degree-specific Graph Neural Networks for Node and Graph Classification](https://mlsanity.com/paper/1906.02319/) (2019)
- [Semi-Implicit Graph Variational Auto-Encoders](https://mlsanity.com/paper/1908.07078/) (2019)
- [Multi-dimensional Graph Convolutional Networks](https://mlsanity.com/paper/1808.06099/) (2018)
- [Exploring the Semantic Content of Unsupervised Graph Embeddings: An Empirical Study](https://mlsanity.com/paper/1806.07464/) (2018)

## Built on by (most cited first, 1 of 1)

- [TopoDetect: Framework for Topological Features Detection in Graph Embeddings](https://mlsanity.com/paper/2110.04173/) (2021)

## Abstract (arXiv)

While representation learning has yielded a great success on many graph learning tasks, there is little understanding behind the structures that are being captured by these embeddings. For example, we wonder if the topological features, such as the Triangle Count, the Degree of the node and other centrality measures are concretely encoded in the embeddings. Furthermore, we ask if the presence of these structures in the embeddings is necessary for a better performance on the downstream tasks, such as clustering and classification. To address these questions, we conduct an extensive empirical study over three classes of unsupervised graph embedding models and seven different variants of Graph Autoencoders. Our results show that five topological features: the Degree, the Local Clustering Score, the Betweenness Centrality, the Eigenvector Centrality, and Triangle Count are concretely preserved in the first layer of the graph autoencoder that employs the SUM aggregation rule, under the condition that the model preserves the second-order proximity. We supplement further evidence for the presence of these features by revealing a hierarchy in the distribution of the topological features in the embeddings of the aforementioned model. We also show that a model with such properties can outperform other models on certain downstream tasks, especially when the preserved features are relevant to the task at hand. Finally, we evaluate the suitability of our findings through a test case study related to social influence prediction.