# Generating the Graph Gestalt: Kernel-Regularized Graph Representation Learning

arXiv: https://arxiv.org/abs/2106.15239 · HTML: https://mlsanity.com/paper/2106.15239/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 33 references that are in the map.
- First posted on arXiv 29 Jun 2021.

## Builds on (most cited first, 16 of 16)

- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [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)
- [Graph Transformer Networks](https://mlsanity.com/paper/1911.06455/) (2019)
- [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)
- [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)
- [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)
- [Graph Kernels: A Survey](https://mlsanity.com/paper/1904.12218/) (2019)
- [Stochastic Blockmodels meet Graph Neural Networks](https://mlsanity.com/paper/1905.05738/) (2019)
- [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)
- [Matrix Completion With Variational Graph Autoencoders: Application in Hyperlocal Air Quality Inference](https://mlsanity.com/paper/1811.01662/) (2018)

## Abstract (arXiv)

Recent work on graph generative models has made remarkable progress towards generating increasingly realistic graphs, as measured by global graph features such as degree distribution, density, and clustering coefficients. Deep generative models have also made significant advances through better modelling of the local correlations in the graph topology, which have been very useful for predicting unobserved graph components, such as the existence of a link or the class of a node, from nearby observed graph components. A complete scientific understanding of graph data should address both global and local structure. In this paper, we propose a joint model for both as complementary objectives in a graph VAE framework. Global structure is captured by incorporating graph kernels in a probabilistic model whose loss function is closely related to the maximum mean discrepancy(MMD) between the global structures of the reconstructed and the input graphs. The ELBO objective derived from the model regularizes a standard local link reconstruction term with an MMD term. Our experiments demonstrate a significant improvement in the realism of the generated graph structures, typically by 1-2 orders of magnitude of graph structure metrics, compared to leading graph VAEand GAN models. Local link reconstruction improves as well in many cases.