# On the Power of Edge Independent Graph Models

arXiv: https://arxiv.org/abs/2111.00048 · HTML: https://mlsanity.com/paper/2111.00048/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 46 references that are in the map.
- First posted on arXiv 29 Oct 2021.

## Builds on (most cited first, 10 of 10)

- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [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)
- [Learning Deep Generative Models of Graphs](https://mlsanity.com/paper/1803.03324/) (2018)
- [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)
- [The impossibility of low rank representations for triangle-rich complex networks](https://mlsanity.com/paper/2003.12635/) (2020)
- [Node Embeddings and Exact Low-Rank Representations of Complex Networks](https://mlsanity.com/paper/2006.05592/) (2020)

## Built on by (most cited first, 16 of 16)

- [Efficient and Degree-Guided Graph Generation via Discrete Diffusion Modeling](https://mlsanity.com/paper/2305.04111/) (2023)
- [GraphMaker: Can Diffusion Models Generate Large Attributed Graphs?](https://mlsanity.com/paper/2310.13833/) (2023)
- [HiGen: Hierarchical Graph Generative Networks](https://mlsanity.com/paper/2305.19337/) (2023)
- [EDGE++: Improved Training and Sampling of EDGE](https://mlsanity.com/paper/2310.14441/) (2023)
- [On the Role of Edge Dependency in Graph Generative Models](https://mlsanity.com/paper/2312.03691/) (2023)
- [Random Walk Diffusion for Efficient Large-Scale Graph Generation](https://mlsanity.com/paper/2408.04461/) (2024)
- [Implications of sparsity and high triangle density for graph representation learning](https://mlsanity.com/paper/2210.15277/) (2022)
- [Leveraging Graph Diffusion Models for Network Refinement Tasks](https://mlsanity.com/paper/2311.17856/) (2023)
- [SteinGen: Generating Fidelitous and Diverse Graph Samples](https://mlsanity.com/paper/2403.18578/) (2024)
- [An Optimal Transport Approach for Network Regression](https://mlsanity.com/paper/2406.12204/) (2024)
- [Spectral embedding and the latent geometry of multipartite networks](https://mlsanity.com/paper/2202.03945/) (2022)
- [Edge Probability Graph Models Beyond Edge Independency: Concepts, Analyses, and Algorithms](https://mlsanity.com/paper/2405.16726/) (2024)
- [Uncovering Locally Low-dimensional Structure in Networks by Locally Optimal Spectral Embedding](https://mlsanity.com/paper/2603.11965/) (2026)
- [Discrete Diffusion for Large Graph Generation via Structural Candidate Restriction](https://mlsanity.com/paper/2610.04056/) (2026)
- [When Edge Independence Fails: Joint Graph Diffusion with Latent Sociability Priors](https://mlsanity.com/paper/2610.13765/) (2026)
- [Your Discrete Graph Diffusion Model is Secretly Memorizing](https://mlsanity.com/paper/2610.13786/) (2026)

## Abstract (arXiv)

Why do many modern neural-network-based graph generative models fail to reproduce typical real-world network characteristics, such as high triangle density? In this work we study the limitations of edge independent random graph models, in which each edge is added to the graph independently with some probability. Such models include both the classic Erd"os-R'enyi and stochastic block models, as well as modern generative models such as NetGAN, variational graph autoencoders, and CELL. We prove that subject to a bounded overlap condition, which ensures that the model does not simply memorize a single graph, edge independent models are inherently limited in their ability to generate graphs with high triangle and other subgraph densities. Notably, such high densities are known to appear in real-world social networks and other graphs. We complement our negative results with a simple generative model that balances overlap and accuracy, performing comparably to more complex models in reconstructing many graph statistics.