# Modularity-Aware Graph Autoencoders for Joint Community Detection and Link Prediction

arXiv: https://arxiv.org/abs/2202.00961 · HTML: https://mlsanity.com/paper/2202.00961/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 54 of its 109 references that are in the map.
- First posted on arXiv 2 Feb 2022.

## Builds on (most cited first, 30 of 54)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Junction Tree Variational Autoencoder for Molecular Graph Generation](https://mlsanity.com/paper/1802.04364/) (2018)
- [FastGCN: Fast Learning with Graph Convolutional Networks via Importance Sampling](https://mlsanity.com/paper/1801.10247/) (2018)
- [Cluster-GCN: An Efficient Algorithm for Training Deep and Large Graph Convolutional Networks](https://mlsanity.com/paper/1905.07953/) (2019)
- [Representation Learning on Graphs: Methods and Applications](https://mlsanity.com/paper/1709.05584/) (2017)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Tutorial on Variational Autoencoders](https://mlsanity.com/paper/1606.05908/) (2016)
- [GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoders](https://mlsanity.com/paper/1802.03480/) (2018)
- [Community Detection and Stochastic Block Models](https://mlsanity.com/paper/1703.10146/) (2017)
- [Graph Self-Supervised Learning: A Survey](https://mlsanity.com/paper/2103.00111/) (2021)
- [CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filters](https://mlsanity.com/paper/1705.07664/) (2017)
- [Constrained Graph Variational Autoencoders for Molecule Design](https://mlsanity.com/paper/1805.09076/) (2018)
- [Self-Supervised Learning of Graph Neural Networks: A Unified Review](https://mlsanity.com/paper/2102.10757/) (2021)
- [Self-supervised Learning on Graphs: Contrastive, Generative,or Predictive](https://mlsanity.com/paper/2105.07342/) (2021)
- [Neural Expectation Maximization](https://mlsanity.com/paper/1708.03498/) (2017)
- [When Does Self-Supervision Help Graph Convolutional Networks?](https://mlsanity.com/paper/2006.09136/) (2020)
- [Graphite: Iterative Generative Modeling of Graphs](https://mlsanity.com/paper/1803.10459/) (2018)
- [Multi-Stage Self-Supervised Learning for Graph Convolutional Networks on Graphs with Few Labels](https://mlsanity.com/paper/1902.11038/) (2019)

## Built on by (most cited first, 22 of 22)

- [Revisiting Modularity Maximization for Graph Clustering: A Contrastive Learning Perspective](https://mlsanity.com/paper/2406.14288/) (2024)
- [PTGB: Pre-Train Graph Neural Networks for Brain Network Analysis](https://mlsanity.com/paper/2305.14376/) (2023)
- [TransformerG2G: Adaptive time-stepping for learning temporal graph embeddings using transformers](https://mlsanity.com/paper/2307.02588/) (2023)
- [DINE: Dimensional Interpretability of Node Embeddings](https://mlsanity.com/paper/2310.01162/) (2023)
- [On Exploring Node-feature and Graph-structure Diversities for Node Drop Graph Pooling](https://mlsanity.com/paper/2306.12726/) (2023)
- [Signed Graph Autoencoder for Explainable and Polarization-Aware Network Embeddings](https://mlsanity.com/paper/2409.10452/) (2024)
- [EGRC-Net: Embedding-induced Graph Refinement Clustering Network](https://mlsanity.com/paper/2211.10627/) (2022)
- [Modularity in Deep Learning: A Survey](https://mlsanity.com/paper/2310.01154/) (2023)
- [Exploring Large Action Sets with Hyperspherical Embeddings using von Mises-Fisher Sampling](https://mlsanity.com/paper/2507.00518/) (2025)
- [Studying Cross-cluster Modularity in Neural Networks](https://mlsanity.com/paper/2502.02470/) (2025)
- [New Frontiers in Graph Autoencoders: Joint Community Detection and Link Prediction](https://mlsanity.com/paper/2211.08972/) (2022)
- [Rethinking the positive role of cluster structure in complex networks for link prediction tasks](https://mlsanity.com/paper/2211.02396/) (2022)
- [Heterophilous Distribution Propagation for Graph Neural Networks](https://mlsanity.com/paper/2405.20640/) (2024)
- [Modularity aided consistent attributed graph clustering via coarsening](https://mlsanity.com/paper/2407.07128/) (2024)
- [RDSA: A Robust Deep Graph Clustering Framework via Dual Soft Assignment](https://mlsanity.com/paper/2410.21745/) (2024)
- [To Share or Not to Share: Investigating Weight Sharing in Variational Graph Autoencoders](https://mlsanity.com/paper/2502.16724/) (2025)
- [Directed Link Prediction using GNN with Local and Global Feature Fusion](https://mlsanity.com/paper/2506.20235/) (2025)
- [GraphSB: Boosting Imbalanced Node Classification on Graphs through Structural Balance](https://mlsanity.com/paper/2511.10022/) (2025)
- [Dual Refinement Cycle Learning: Unsupervised Text Classification of Mamba and Community Detection on Text Attributed Graph](https://mlsanity.com/paper/2512.07100/) (2025)
- [GraphSB: Boosting Imbalanced Node Classification on Graphs through Structural Balance](https://mlsanity.com/paper/2601.19352/) (2026)
- [Graph Neural Networks for Community Detection in Graph Signal Analysis](https://mlsanity.com/paper/2605.19733/) (2026)
- [ModTGCN: Modularity-aware Graph Neural Networks for Text Classification](https://mlsanity.com/paper/2606.23694/) (2026)

## Abstract (arXiv)

Graph autoencoders (GAE) and variational graph autoencoders (VGAE) emerged as powerful methods for link prediction. Their performances are less impressive on community detection problems where, according to recent and concurring experimental evaluations, they are often outperformed by simpler alternatives such as the Louvain method. It is currently still unclear to which extent one can improve community detection with GAE and VGAE, especially in the absence of node features. It is moreover uncertain whether one could do so while simultaneously preserving good performances on link prediction. In this paper, we show that jointly addressing these two tasks with high accuracy is possible. For this purpose, we introduce and theoretically study a community-preserving message passing scheme, doping our GAE and VGAE encoders by considering both the initial graph structure and modularity-based prior communities when computing embedding spaces. We also propose novel training and optimization strategies, including the introduction of a modularity-inspired regularizer complementing the existing reconstruction losses for joint link prediction and community detection. We demonstrate the empirical effectiveness of our approach, referred to as Modularity-Aware GAE and VGAE, through in-depth experimental validation on various real-world graphs.