# GC-Flow: A Graph-Based Flow Network for Effective Clustering

arXiv: https://arxiv.org/abs/2305.17284 · HTML: https://mlsanity.com/paper/2305.17284/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 52 of its 66 references that are in the map.
- First posted on arXiv 26 May 2023.

## Builds on (most cited first, 30 of 52)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Graph Convolutional Neural Networks for Web-Scale Recommender Systems](https://mlsanity.com/paper/1806.01973/) (2018)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Gated Graph Sequence Neural Networks](https://mlsanity.com/paper/1511.05493/) (2015)
- [Image-based Recommendations on Styles and Substitutes](https://mlsanity.com/paper/1506.04757/) (2015)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Contrastive Multi-View Representation Learning on Graphs](https://mlsanity.com/paper/2006.05582/) (2020)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [GraphSAINT: Graph Sampling Based Inductive Learning Method](https://mlsanity.com/paper/1907.04931/) (2019)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)

## Built on by (most cited first, 5 of 5)

- [LSEnet: Lorentz Structural Entropy Neural Network for Deep Graph Clustering](https://mlsanity.com/paper/2405.11801/) (2024)
- [Parametric Augmentation for Time Series Contrastive Learning](https://mlsanity.com/paper/2402.10434/) (2024)
- [ASIL: Augmented Structural Information Learning for Deep Graph Clustering in Hyperbolic Space](https://mlsanity.com/paper/2504.09970/) (2025)
- [K-GBS3FCM -- KNN Graph-Based Safe Semi-Supervised Fuzzy C-Means](https://mlsanity.com/paper/2411.14728/) (2024)
- [Beyond Unimodal Bases: Pullback Geometry for Multimodal Data](https://mlsanity.com/paper/2610.00708/) (2026)

## Abstract (arXiv)

Graph convolutional networks (GCNs) are discriminative models that directly model the class posterior p(y|x) for semi-supervised classification of graph data. While being effective, as a representation learning approach, the node representations extracted from a GCN often miss useful information for effective clustering, because the objectives are different. In this work, we design normalizing flows that replace GCN layers, leading to a generative model that models both the class conditional likelihood p(x|y) and the class prior p(y). The resulting neural network, GC-Flow, retains the graph convolution operations while being equipped with a Gaussian mixture representation space. It enjoys two benefits: it not only maintains the predictive power of GCN, but also produces well-separated clusters, due to the structuring of the representation space. We demonstrate these benefits on a variety of benchmark data sets. Moreover, we show that additional parameterization, such as that on the adjacency matrix used for graph convolutions, yields additional improvement in clustering.