# TD-GEN: Graph Generation With Tree Decomposition

arXiv: https://arxiv.org/abs/2106.10656 · HTML: https://mlsanity.com/paper/2106.10656/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 33 references that are in the map.
- First posted on arXiv 20 Jun 2021.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [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)
- [GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoders](https://mlsanity.com/paper/1802.03480/) (2018)
- [Graph Convolutional Policy Network for Goal-Directed Molecular Graph Generation](https://mlsanity.com/paper/1806.02473/) (2018)
- [GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generation](https://mlsanity.com/paper/2001.09382/) (2020)
- [Permutation Invariant Graph Generation via Score-Based Generative Modeling](https://mlsanity.com/paper/2003.00638/) (2020)
- [Efficient Graph Generation with Graph Recurrent Attention Networks](https://mlsanity.com/paper/1910.00760/) (2019)
- [Learning Deep Generative Models of Graphs](https://mlsanity.com/paper/1803.03324/) (2018)
- [Hierarchical Generation of Molecular Graphs using Structural Motifs](https://mlsanity.com/paper/2002.03230/) (2020)
- [MoFlow: An Invertible Flow Model for Generating Molecular Graphs](https://mlsanity.com/paper/2006.10137/) (2020)
- [NetGAN: Generating Graphs via Random Walks](https://mlsanity.com/paper/1803.00816/) (2018)
- [Graph Normalizing Flows](https://mlsanity.com/paper/1905.13177/) (2019)
- [Variational Graph Recurrent Neural Networks](https://mlsanity.com/paper/1908.09710/) (2019)
- [Scalable Deep Generative Modeling for Sparse Graphs](https://mlsanity.com/paper/2006.15502/) (2020)
- [Order Matters: Probabilistic Modeling of Node Sequence for Graph Generation](https://mlsanity.com/paper/2106.06189/) (2021)
- [An Experimental Study of the Treewidth of Real-World Graph Data (Extended Version)](https://mlsanity.com/paper/1901.06862/) (2019)
- [Graph Generation with Variational Recurrent Neural Network](https://mlsanity.com/paper/1910.01743/) (2019)
- [A Temporal Tree Decomposition for Generating Temporal Graphs](https://mlsanity.com/paper/1706.09480/) (2017)

## Built on by (most cited first, 3 of 3)

- [MAGNet: Motif-Agnostic Generation of Molecules from Shapes](https://mlsanity.com/paper/2305.19303/) (2023)
- [HiGen: Hierarchical Graph Generative Networks](https://mlsanity.com/paper/2305.19337/) (2023)
- [Autoregressive Frontier Expansion: Growing Trees with Graph Machine Learning](https://mlsanity.com/paper/2609.38506/) (2026)

## Abstract (arXiv)

We propose TD-GEN, a graph generation framework based on tree decomposition, and introduce a reduced upper bound on the maximum number of decisions needed for graph generation. The framework includes a permutation invariant tree generation model which forms the backbone of graph generation. Tree nodes are supernodes, each representing a cluster of nodes in the graph. Graph nodes and edges are incrementally generated inside the clusters by traversing the tree supernodes, respecting the structure of the tree decomposition, and following node sharing decisions between the clusters. Finally, we discuss the shortcomings of standard evaluation criteria based on statistical properties of the generated graphs as performance measures. We propose to compare the performance of models based on likelihood. Empirical results on a variety of standard graph generation datasets demonstrate the superior performance of our method.