# Non-Dissipative Graph Propagation for Non-Local Community Detection

arXiv: https://arxiv.org/abs/2508.14097 · HTML: https://mlsanity.com/paper/2508.14097/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 37 of its 57 references that are in the map.
- First posted on arXiv 15 Aug 2025.

## Builds on (most cited first, 30 of 37)

- [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)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Recipe for a General, Powerful, Scalable Graph Transformer](https://mlsanity.com/paper/2205.12454/) (2022)
- [A Generalization of Transformer Networks to Graphs](https://mlsanity.com/paper/2012.09699/) (2020)
- [Contrastive Multi-View Representation Learning on Graphs](https://mlsanity.com/paper/2006.05582/) (2020)
- [On the Bottleneck of Graph Neural Networks and its Practical Implications](https://mlsanity.com/paper/2006.05205/) (2020)
- [Deep Graph Contrastive Representation Learning](https://mlsanity.com/paper/2006.04131/) (2020)
- [Ups and Downs: Modeling the Visual Evolution of Fashion Trends with One-Class Collaborative Filtering](https://mlsanity.com/paper/1602.01585/) (2016)
- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [Stable Architectures for Deep Neural Networks](https://mlsanity.com/paper/1705.03341/) (2017)
- [Long Range Graph Benchmark](https://mlsanity.com/paper/2206.08164/) (2022)
- [GRAND: Graph Neural Diffusion](https://mlsanity.com/paper/2106.10934/) (2021)
- [Graph Neural Networks for Graphs with Heterophily: A Survey](https://mlsanity.com/paper/2202.07082/) (2022)
- [Graph Clustering with Graph Neural Networks](https://mlsanity.com/paper/2006.16904/) (2020)
- [Attributed Graph Clustering: A Deep Attentional Embedding Approach](https://mlsanity.com/paper/1906.06532/) (2019)
- [Graph-Coupled Oscillator Networks](https://mlsanity.com/paper/2202.02296/) (2022)
- [Towards Unsupervised Deep Graph Structure Learning](https://mlsanity.com/paper/2201.06367/) (2022)
- [AntisymmetricRNN: A Dynamical System View on Recurrent Neural Networks](https://mlsanity.com/paper/1902.09689/) (2019)
- [A Gentle Introduction to Deep Learning for Graphs](https://mlsanity.com/paper/1912.12693/) (2019)
- [PDE-GCN: Novel Architectures for Graph Neural Networks Motivated by Partial Differential Equations](https://mlsanity.com/paper/2108.01938/) (2021)
- [DRew: Dynamically Rewired Message Passing with Delay](https://mlsanity.com/paper/2305.08018/) (2023)
- [GeomGCL: Geometric Graph Contrastive Learning for Molecular Property Prediction](https://mlsanity.com/paper/2109.11730/) (2021)
- [Anti-Symmetric DGN: a stable architecture for Deep Graph Networks](https://mlsanity.com/paper/2210.09789/) (2022)
- [GREAD: Graph Neural Reaction-Diffusion Networks](https://mlsanity.com/paper/2211.14208/) (2022)
- [A Fractional Graph Laplacian Approach to Oversmoothing](https://mlsanity.com/paper/2305.13084/) (2023)
- [N2D: (Not Too) Deep Clustering via Clustering the Local Manifold of an Autoencoded Embedding](https://mlsanity.com/paper/1908.05968/) (2019)
- [On Oversquashing in Graph Neural Networks Through the Lens of Dynamical Systems](https://mlsanity.com/paper/2405.01009/) (2024)

## Abstract (arXiv)

Community detection in graphs aims to cluster nodes into meaningful groups, a task particularly challenging in heterophilic graphs, where nodes sharing similarities and membership to the same community are typically distantly connected. This is particularly evident when this task is tackled by graph neural networks, since they rely on an inherently local message passing scheme to learn the node representations that serve to cluster nodes into communities. In this work, we argue that the ability to propagate long-range information during message passing is key to effectively perform community detection in heterophilic graphs. To this end, we introduce the Unsupervised Antisymmetric Graph Neural Network (uAGNN), a novel unsupervised community detection approach leveraging non-dissipative dynamical systems to ensure stability and to propagate long-range information effectively. By employing antisymmetric weight matrices, uAGNN captures both local and global graph structures, overcoming the limitations posed by heterophilic scenarios. Extensive experiments across ten datasets demonstrate uAGNN's superior performance in high and medium heterophilic settings, where traditional methods fail to exploit long-range dependencies. These results highlight uAGNN's potential as a powerful tool for unsupervised community detection in diverse graph environments.