# Revisiting Modularity Maximization for Graph Clustering: A Contrastive Learning Perspective

arXiv: https://arxiv.org/abs/2406.14288 · HTML: https://mlsanity.com/paper/2406.14288/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 49 references that are in the map.
- First posted on arXiv 20 Jun 2024.

## Builds on (most cited first, 28 of 28)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [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)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [Unsupervised Feature Learning via Non-Parametric Instance-level Discrimination](https://mlsanity.com/paper/1805.01978/) (2018)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Learning deep representations by mutual information estimation and maximization](https://mlsanity.com/paper/1808.06670/) (2018)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Contrastive Multi-View Representation Learning on Graphs](https://mlsanity.com/paper/2006.05582/) (2020)
- [Deep Graph Contrastive Representation Learning](https://mlsanity.com/paper/2006.04131/) (2020)
- [Understanding the Behaviour of Contrastive Loss](https://mlsanity.com/paper/2012.09740/) (2020)
- [From Louvain to Leiden: guaranteeing well-connected communities](https://mlsanity.com/paper/1810.08473/) (2018)
- [Graph Clustering with Graph Neural Networks](https://mlsanity.com/paper/2006.16904/) (2020)
- [Symmetric Graph Convolutional Autoencoder for Unsupervised Graph Representation Learning](https://mlsanity.com/paper/1908.02441/) (2019)
- [Augmentation-Free Self-Supervised Learning on Graphs](https://mlsanity.com/paper/2112.02472/) (2021)
- [Adaptive Graph Encoder for Attributed Graph Embedding](https://mlsanity.com/paper/2007.01594/) (2020)
- [What's Behind the Mask: Understanding Masked Graph Modeling for Graph Autoencoders](https://mlsanity.com/paper/2205.10053/) (2022)
- [Cluster-guided Contrastive Graph Clustering Network](https://mlsanity.com/paper/2301.01098/) (2023)
- [InfoNCE Loss Provably Learns Cluster-Preserving Representations](https://mlsanity.com/paper/2302.07920/) (2023)
- [Modularity-Aware Graph Autoencoders for Joint Community Detection and Link Prediction](https://mlsanity.com/paper/2202.00961/) (2022)
- [DGCLUSTER: A Neural Framework for Attributed Graph Clustering via Modularity Maximization](https://mlsanity.com/paper/2312.12697/) (2023)
- [Graph Neural Network Encoding for Community Detection in Attribute Networks](https://mlsanity.com/paper/2006.03996/) (2020)
- [Rethinking and Simplifying Bootstrapped Graph Latents](https://mlsanity.com/paper/2312.02619/) (2023)

## Built on by (most cited first, 18 of 18)

- [Deep Cut-informed Graph Embedding and Clustering](https://mlsanity.com/paper/2503.06635/) (2025)
- [ASIL: Augmented Structural Information Learning for Deep Graph Clustering in Hyperbolic Space](https://mlsanity.com/paper/2504.09970/) (2025)
- [Bridging Academia and Industry: A Comprehensive Benchmark for Attributed Graph Clustering](https://mlsanity.com/paper/2602.08519/) (2026)
- [KAT-Coder-V2.5 Technical Report](https://mlsanity.com/paper/2607.05471/) (2026)
- [Community-Level Modeling of Gyral Folding Patterns for Robust and Anatomically Informed Individualized Brain Mapping](https://mlsanity.com/paper/2602.01482/) (2026)
- [Node Role-Guided LLMs for Dynamic Graph Clustering](https://mlsanity.com/paper/2603.13799/) (2026)
- [Beyond the Academic Monoculture: A Unified Framework and Industrial Perspective for Attributed Graph Clustering](https://mlsanity.com/paper/2603.20829/) (2026)
- [Structure-enhanced Contrastive Learning for Graph Clustering](https://mlsanity.com/paper/2408.09790/) (2024)
- [RDSA: A Robust Deep Graph Clustering Framework via Dual Soft Assignment](https://mlsanity.com/paper/2410.21745/) (2024)
- [Contrastive clustering based on regular equivalence for influential node identification in complex networks](https://mlsanity.com/paper/2509.02609/) (2025)
- [Dual Refinement Cycle Learning: Unsupervised Text Classification of Mamba and Community Detection on Text Attributed Graph](https://mlsanity.com/paper/2512.07100/) (2025)
- [Optimization-Free Graph Embedding via Distributional Kernel for Community Detection](https://mlsanity.com/paper/2602.13634/) (2026)
- [ARMA-C3: A Contrastive ARMA Convolutional Framework for Unsupervised and Semi-supervised Classification](https://mlsanity.com/paper/2605.25657/) (2026)
- [Robust Contrastive Graph Clustering with Adaptive Local-Global Integration](https://mlsanity.com/paper/2605.28209/) (2026)
- [Alcmean's: Unsupervised community detection using local Laplacian, automatic detection of the number of centers](https://mlsanity.com/paper/2606.09100/) (2026)
- [Bridge the Gaps: Heterogeneous Attributed Graph Clustering via Quaternion Representation Learning](https://mlsanity.com/paper/2606.23199/) (2026)
- [RHEA: Reliability-Harmonized Reconstruction and Assignment for Robust Multimodal-Attributed Graph Clustering](https://mlsanity.com/paper/2608.00621/) (2026)
- [Topology-induced Operators Reveal Complementary Graph Representations without Training](https://mlsanity.com/paper/2609.08152/) (2026)

## Abstract (arXiv)

Graph clustering, a fundamental and challenging task in graph mining, aims to classify nodes in a graph into several disjoint clusters. In recent years, graph contrastive learning (GCL) has emerged as a dominant line of research in graph clustering and advances the new state-of-the-art. However, GCL-based methods heavily rely on graph augmentations and contrastive schemes, which may potentially introduce challenges such as semantic drift and scalability issues. Another promising line of research involves the adoption of modularity maximization, a popular and effective measure for community detection, as the guiding principle for clustering tasks. Despite the recent progress, the underlying mechanism of modularity maximization is still not well understood. In this work, we dig into the hidden success of modularity maximization for graph clustering. Our analysis reveals the strong connections between modularity maximization and graph contrastive learning, where positive and negative examples are naturally defined by modularity. In light of our results, we propose a community-aware graph clustering framework, coined MAGI, which leverages modularity maximization as a contrastive pretext task to effectively uncover the underlying information of communities in graphs, while avoiding the problem of semantic drift. Extensive experiments on multiple graph datasets verify the effectiveness of MAGI in terms of scalability and clustering performance compared to state-of-the-art graph clustering methods. Notably, MAGI easily scales a sufficiently large graph with 100M nodes while outperforming strong baselines.