# Dirichlet Graph Variational Autoencoder

arXiv: https://arxiv.org/abs/2010.04408 · HTML: https://mlsanity.com/paper/2010.04408/

## Key facts

- Cited by 40 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Oct 2020.

## Built on by (most cited first, 30 of 40)

- [Self-Supervised Learning of Graph Neural Networks: A Unified Review](https://mlsanity.com/paper/2102.10757/) (2021)
- [Efficient and Degree-Guided Graph Generation via Discrete Diffusion Modeling](https://mlsanity.com/paper/2305.04111/) (2023)
- [Graph-based Semi-supervised Learning: A Comprehensive Review](https://mlsanity.com/paper/2102.13303/) (2021)
- [A Survey on Deep Graph Generation: Methods and Applications](https://mlsanity.com/paper/2203.06714/) (2022)
- [A Survey of Deep Graph Clustering: Taxonomy, Challenge, Application, and Open Resource](https://mlsanity.com/paper/2211.12875/) (2022)
- [Modularity-Aware Graph Autoencoders for Joint Community Detection and Link Prediction](https://mlsanity.com/paper/2202.00961/) (2022)
- [NVDiff: Graph Generation through the Diffusion of Node Vectors](https://mlsanity.com/paper/2211.10794/) (2022)
- [Deconvolutional Networks on Graph Data](https://mlsanity.com/paper/2110.15528/) (2021)
- [Contrastive Graph Clustering in Curvature Spaces](https://mlsanity.com/paper/2305.03555/) (2023)
- [Wiener Graph Deconvolutional Network Improves Graph Self-Supervised Learning](https://mlsanity.com/paper/2206.12933/) (2022)
- [A Convergent Single-Loop Algorithm for Relaxation of Gromov-Wasserstein in Graph Data](https://mlsanity.com/paper/2303.06595/) (2023)
- [Mask-GVAE: Blind Denoising Graphs via Partition](https://mlsanity.com/paper/2102.04228/) (2021)
- [Node-Aligned Graph-to-Graph (NAG2G): Elevating Template-Free Deep Learning Approaches in Single-Step Retrosynthesis](https://mlsanity.com/paper/2309.15798/) (2023)
- [A Survey on Self-Supervised Graph Foundation Models: Knowledge-Based Perspective](https://mlsanity.com/paper/2403.16137/) (2024)
- [Neural Graph Generator: Feature-Conditioned Graph Generation using Latent Diffusion Models](https://mlsanity.com/paper/2403.01535/) (2024)
- [Continual Learning with Dirichlet Generative-based Rehearsal](https://mlsanity.com/paper/2309.06917/) (2023)
- [Hyperspectral Pixel Unmixing with Latent Dirichlet Variational Autoencoder](https://mlsanity.com/paper/2203.01327/) (2022)
- [A Contrastive Variational Graph Auto-Encoder for Node Clustering](https://mlsanity.com/paper/2312.16830/) (2023)
- [Uncertainty Quantification on Graph Learning: A Survey](https://mlsanity.com/paper/2404.14642/) (2024)
- [Signed Graph Autoencoder for Explainable and Polarization-Aware Network Embeddings](https://mlsanity.com/paper/2409.10452/) (2024)
- [Principled Latent Diffusion for Graphs via Laplacian Autoencoders](https://mlsanity.com/paper/2601.13780/) (2026)
- [Interpretable Node Representation with Attribute Decoding](https://mlsanity.com/paper/2212.01682/) (2022)
- [EDGE++: Improved Training and Sampling of EDGE](https://mlsanity.com/paper/2310.14441/) (2023)
- [Gen-C: Populating Virtual Worlds with Generative Crowds](https://mlsanity.com/paper/2504.01924/) (2025)
- [Deep Graph Clustering via Mutual Information Maximization and Mixture Model](https://mlsanity.com/paper/2205.05168/) (2022)
- [SCGG: A Deep Structure-Conditioned Graph Generative Model](https://mlsanity.com/paper/2209.09681/) (2022)
- [Modeling and design of heterogeneous hierarchical bioinspired spider web structures using generative deep learning and additive manufacturing](https://mlsanity.com/paper/2304.05137/) (2023)
- [BN-Pool: Bayesian Nonparametric Pooling for Graphs](https://mlsanity.com/paper/2501.09821/) (2025)
- [Operator Autoencoders: Learning Physical Operations on Encoded Molecular Graphs](https://mlsanity.com/paper/2105.12295/) (2021)
- [Graph2Graph Learning with Conditional Autoregressive Models](https://mlsanity.com/paper/2106.03236/) (2021)

## Abstract (arXiv)

Graph Neural Networks (GNNs) and Variational Autoencoders (VAEs) have been widely used in modeling and generating graphs with latent factors. However, there is no clear explanation of what these latent factors are and why they perform well. In this work, we present Dirichlet Graph Variational Autoencoder (DGVAE) with graph cluster memberships as latent factors. Our study connects VAEs based graph generation and balanced graph cut, and provides a new way to understand and improve the internal mechanism of VAEs based graph generation. Specifically, we first interpret the reconstruction term of DGVAE as balanced graph cut in a principled way. Furthermore, motivated by the low pass characteristics in balanced graph cut, we propose a new variant of GNN named Heatts to encode the input graph into cluster memberships. Heatts utilizes the Taylor series for fast computation of heat kernels and has better low pass characteristics than Graph Convolutional Networks (GCN). Through experiments on graph generation and graph clustering, we demonstrate the effectiveness of our proposed framework.