# Reinforcement Learning for Graph Generation under a Hard Assortativity Constraint

arXiv: https://arxiv.org/abs/2605.23285 · HTML: https://mlsanity.com/paper/2605.23285/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL for games and combinatorial optimization, one of 15 directions in Deep reinforcement learning methods.
- Builds on 19 of its 56 references that are in the map.
- First posted on arXiv 22 May 2026.

## Placed in

- Deep reinforcement learning methods / [RL for games and combinatorial optimization](https://mlsanity.com/deeprl/rl-for-games-and-combinatorial-optimization/)

## Builds on (most cited first, 19 of 19)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Curiosity-driven Exploration by Self-supervised Prediction](https://mlsanity.com/paper/1705.05363/) (2017)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [Junction Tree Variational Autoencoder for Molecular Graph Generation](https://mlsanity.com/paper/1802.04364/) (2018)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [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)
- [A Closer Look at Invalid Action Masking in Policy Gradient Algorithms](https://mlsanity.com/paper/2006.14171/) (2020)
- [SPECTRE: Spectral Conditioning Helps to Overcome the Expressivity Limits of One-shot Graph Generators](https://mlsanity.com/paper/2204.01613/) (2022)
- [Action Branching Architectures for Deep Reinforcement Learning](https://mlsanity.com/paper/1711.08946/) (2017)
- [GraphGDP: Generative Diffusion Processes for Permutation Invariant Graph Generation](https://mlsanity.com/paper/2212.01842/) (2022)
- [Configuring Random Graph Models with Fixed Degree Sequences](https://mlsanity.com/paper/1608.00607/) (2016)
- [Goal-directed graph construction using reinforcement learning](https://mlsanity.com/paper/2001.11279/) (2020)
- [Unbiased sampling of network ensembles](https://mlsanity.com/paper/1406.1197/) (2014)
- [Exact sampling of graphs with prescribed degree correlations](https://mlsanity.com/paper/1503.06725/) (2015)

## Abstract (arXiv)

Generating graph ensembles with precisely controlled structural properties is central to investigating how network structure shapes function. Canonical ensembles impose constraints only in expectation (soft constraints), letting individual realizations fluctuate around the target, whereas enforcing hard constraints with prescribed precision in every realization remains challenging beyond fixing the degree sequence. Here we show that a reinforcement learning framework can drive a graph through degree-preserving rewirings to satisfy a prescribed assortativity, which characterizes the degree--degree correlation of adjacent nodes. By replacing the entropically dominated Metropolis--Hastings random walk with directed transport, the learned policy reduces generation cost by at least an order of magnitude while retaining over 98% of configurational diversity. Trained on small graphs, the framework generalizes across sizes and topologies without retraining, enabling quantitative isolation of secondary observables such as the clustering coefficient. These results establish reinforcement learning as a practical paradigm for hard-constrained graph generation.