# Recovering Barab'asi-Albert Parameters of Graphs through Disentanglement

arXiv: https://arxiv.org/abs/2105.00997 · HTML: https://mlsanity.com/paper/2105.00997/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 19 references that are in the map.
- First posted on arXiv 3 May 2021.

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

- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [MONet: Unsupervised Scene Decomposition and Representation](https://mlsanity.com/paper/1901.11390/) (2019)
- [Learning Deep Generative Models of Graphs](https://mlsanity.com/paper/1803.03324/) (2018)
- [Constrained Graph Variational Autoencoders for Molecule Design](https://mlsanity.com/paper/1805.09076/) (2018)
- [On the Fairness of Disentangled Representations](https://mlsanity.com/paper/1905.13662/) (2019)
- [A Gentle Introduction to Deep Learning for Graphs](https://mlsanity.com/paper/1912.12693/) (2019)
- [Are Disentangled Representations Helpful for Abstract Visual Reasoning?](https://mlsanity.com/paper/1905.12506/) (2019)
- [Counterfactuals uncover the modular structure of deep generative models](https://mlsanity.com/paper/1812.03253/) (2018)
- [Interpretable Deep Graph Generation with Node-Edge Co-Disentanglement](https://mlsanity.com/paper/2006.05385/) (2020)
- [Disentangling Interpretable Generative Parameters of Random and Real-World Graphs](https://mlsanity.com/paper/1910.05639/) (2019)

## Abstract (arXiv)

Classical graph modeling approaches such as ErdHos R'enyi (ER) random graphs or Barab'asi-Albert (BA) graphs, here referred to as stylized models, aim to reproduce properties of real-world graphs in an interpretable way. While useful, graph generation with stylized models requires domain knowledge and iterative trial and error simulation. Previous work by Stoehr et al. (2019) addresses these issues by learning the generation process from graph data, using a disentanglement-focused deep autoencoding framework, more specifically, a β-Variational Autoencoder (β-VAE). While they successfully recover the generative parameters of ER graphs through the model's latent variables, their model performs badly on sequentially generated graphs such as BA graphs, due to their oversimplified decoder. We focus on recovering the generative parameters of BA graphs by replacing their β-VAE decoder with a sequential one. We first learn the generative BA parameters in a supervised fashion using a Graph Neural Network (GNN) and a Random Forest Regressor, by minimizing the squared loss between the true generative parameters and the latent variables. Next, we train a β-VAE model, combining the GNN encoder from the first stage with an LSTM-based decoder with a customized loss.