# Micro and Macro Level Graph Modeling for Graph Variational Auto-Encoders

arXiv: https://arxiv.org/abs/2210.16844 · HTML: https://mlsanity.com/paper/2210.16844/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 58 references that are in the map.
- First posted on arXiv 30 Oct 2022.

## Builds on (most cited first, 28 of 28)

- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Gated Graph Sequence Neural Networks](https://mlsanity.com/paper/1511.05493/) (2015)
- [Junction Tree Variational Autoencoder for Molecular Graph Generation](https://mlsanity.com/paper/1802.04364/) (2018)
- [GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Models](https://mlsanity.com/paper/1802.08773/) (2018)
- [MolGAN: An implicit generative model for small molecular graphs](https://mlsanity.com/paper/1805.11973/) (2018)
- [GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoders](https://mlsanity.com/paper/1802.03480/) (2018)
- [Efficient Graph Generation with Graph Recurrent Attention Networks](https://mlsanity.com/paper/1910.00760/) (2019)
- [NetGAN: Generating Graphs via Random Walks](https://mlsanity.com/paper/1803.00816/) (2018)
- [Graphite: Iterative Generative Modeling of Graphs](https://mlsanity.com/paper/1803.10459/) (2018)
- [Constrained Generation of Semantically Valid Graphs via Regularizing Variational Autoencoders](https://mlsanity.com/paper/1809.02630/) (2018)
- [NeVAE: A Deep Generative Model for Molecular Graphs](https://mlsanity.com/paper/1802.05283/) (2018)
- [GraphGen: A Scalable Approach to Domain-agnostic Labeled Graph Generation](https://mlsanity.com/paper/2001.08184/) (2020)
- [Scalable Deep Generative Modeling for Sparse Graphs](https://mlsanity.com/paper/2006.15502/) (2020)
- [Simple and Effective VAE Training with Calibrated Decoders](https://mlsanity.com/paper/2006.13202/) (2020)
- [On Evaluation Metrics for Graph Generative Models](https://mlsanity.com/paper/2201.09871/) (2022)
- [Graph Kernels: A Survey](https://mlsanity.com/paper/1904.12218/) (2019)
- [Evaluation Metrics for Graph Generative Models: Problems, Pitfalls, and Practical Solutions](https://mlsanity.com/paper/2106.01098/) (2021)
- [RetGK: Graph Kernels based on Return Probabilities of Random Walks](https://mlsanity.com/paper/1809.02670/) (2018)
- [Bayesian Models of Graphs, Arrays and Other Exchangeable Random Structures](https://mlsanity.com/paper/1312.7857/) (2013)
- [Learnable Histogram: Statistical Context Features for Deep Neural Networks](https://mlsanity.com/paper/1804.09398/) (2018)
- [Approximately Counting Triangles in Sublinear Time](https://mlsanity.com/paper/1504.00954/) (2015)
- [How to Count Triangles, without Seeing the Whole Graph](https://mlsanity.com/paper/2006.11947/) (2020)
- [Relational Marginal Problems: Theory and Estimation](https://mlsanity.com/paper/1709.05825/) (2017)
- [Matrix Completion With Variational Graph Autoencoders: Application in Hyperlocal Air Quality Inference](https://mlsanity.com/paper/1811.01662/) (2018)

## Built on by (most cited first, 8 of 8)

- [SwinGNN: Rethinking Permutation Invariance in Diffusion Models for Graph Generation](https://mlsanity.com/paper/2307.01646/) (2023)
- [Backdoor Attacks on Discrete Graph Diffusion Models](https://mlsanity.com/paper/2503.06340/) (2025)
- [GraViti: Graph-Level Variational Autoencoders with Relaxed Permutation Invariance](https://mlsanity.com/paper/2605.16668/) (2026)
- [SANGEA: Scalable and Attributed Network Generation](https://mlsanity.com/paper/2309.15648/) (2023)
- [Leveraging Graph Diffusion Models for Network Refinement Tasks](https://mlsanity.com/paper/2311.17856/) (2023)
- [From Graph Generation to Graph Classification](https://mlsanity.com/paper/2302.07989/) (2023)
- [Computing Expected Motif Counts for Exchangeable Graph Generative Models](https://mlsanity.com/paper/2305.01089/) (2023)
- [Relating-Up: Advancing Graph Neural Networks through Inter-Graph Relationships](https://mlsanity.com/paper/2405.03950/) (2024)

## Abstract (arXiv)

Generative models for graph data are an important research topic in machine learning. Graph data comprise two levels that are typically analyzed separately: node-level properties such as the existence of a link between a pair of nodes, and global aggregate graph-level statistics, such as motif counts. This paper proposes a new multi-level framework that jointly models node-level properties and graph-level statistics, as mutually reinforcing sources of information. We introduce a new micro-macro training objective for graph generation that combines node-level and graph-level losses. We utilize the micro-macro objective to improve graph generation with a GraphVAE, a well-established model based on graph-level latent variables, that provides fast training and generation time for medium-sized graphs. Our experiments show that adding micro-macro modeling to the GraphVAE model improves graph quality scores up to 2 orders of magnitude on five benchmark datasets, while maintaining the GraphVAE generation speed advantage.