# Scalable Generative Modeling of Weighted Graphs

arXiv: https://arxiv.org/abs/2507.23111 · HTML: https://mlsanity.com/paper/2507.23111/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 35 references that are in the map.
- First posted on arXiv 30 Jul 2025.

## Builds on (most cited first, 14 of 14)

- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [Improved Semantic Representations From Tree-Structured Long Short-Term Memory Networks](https://mlsanity.com/paper/1503.00075/) (2015)
- [Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations](https://mlsanity.com/paper/2202.02514/) (2022)
- [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)
- [Graphite: Iterative Generative Modeling of Graphs](https://mlsanity.com/paper/1803.10459/) (2018)
- [Long Short-Term Memory Based Recurrent Neural Network Architectures for Large Vocabulary Speech Recognition](https://mlsanity.com/paper/1402.1128/) (2014)
- [Scalable Deep Generative Modeling for Sparse Graphs](https://mlsanity.com/paper/2006.15502/) (2020)
- [Sparse Training of Discrete Diffusion Models for Graph Generation](https://mlsanity.com/paper/2311.02142/) (2023)
- [Scalable Generative Models for Graphs with Graph Attention Mechanism](https://mlsanity.com/paper/1906.01861/) (2019)
- [Principled, practical, flexible, fast: a new approach to phylogenetic factor analysis](https://mlsanity.com/paper/2107.01246/) (2021)
- [The multiscale self-similarity of the weighted human brain connectome](https://mlsanity.com/paper/2410.06739/) (2024)

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

- [TVGL-CFM:Generating and Forecasting Time-Varying Trajectories of Dynamic Networks with Conditional Flow Matching](https://mlsanity.com/paper/2607.16894/) (2026)
- [High-Resolution Dynamic Functional Connectivity Generation with Graph-Variate Flow Matching](https://mlsanity.com/paper/2609.37037/) (2026)
- [Discrete Diffusion for Large Graph Generation via Structural Candidate Restriction](https://mlsanity.com/paper/2610.04056/) (2026)

## Abstract (arXiv)

Weighted graphs are ubiquitous throughout biology, chemistry, and the social sciences, motivating the development of generative models for abstract weighted graph data using deep neural networks. However, most current deep generative models are either designed for unweighted graphs and are not easily extended to weighted topologies or incorporate edge weights without consideration of a joint distribution with topology. Furthermore, learning a distribution over weighted graphs must account for complex nonlocal dependencies between both the edges of the graph and corresponding weights of each edge. We develop an autoregressive model BiGG-E, a nontrivial extension of the BiGG model, that learns a joint distribution over weighted graphs while still exploiting sparsity to generate a weighted graph with n nodes and m edges in O((n + m)log n) time. Simulation studies and experiments on a variety of benchmark datasets demonstrate that BiGG-E best captures distributions over weighted graphs while remaining scalable and computationally efficient.