# SmoothGNN: Smoothing-aware GNN for Unsupervised Node Anomaly Detection

arXiv: https://arxiv.org/abs/2405.17525 · HTML: https://mlsanity.com/paper/2405.17525/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 40 references that are in the map.
- First posted on arXiv 27 May 2024.

## Builds on (most cited first, 26 of 26)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [Enhancing Graph Neural Network-based Fraud Detectors against Camouflaged Fraudsters](https://mlsanity.com/paper/2008.08692/) (2020)
- [Rethinking Graph Neural Networks for Anomaly Detection](https://mlsanity.com/paper/2205.15508/) (2022)
- [Graph-based Anomaly Detection and Description: A Survey](https://mlsanity.com/paper/1404.4679/) (2014)
- [From Amateurs to Connoisseurs: Modeling the Evolution of User Expertise through Online Reviews](https://mlsanity.com/paper/1303.4402/) (2013)
- [BOND: Benchmarking Unsupervised Outlier Node Detection on Static Attributed Graphs](https://mlsanity.com/paper/2206.10071/) (2022)
- [DGraph: A Large-Scale Financial Dataset for Graph Anomaly Detection](https://mlsanity.com/paper/2207.03579/) (2022)
- [GADBench: Revisiting and Benchmarking Supervised Graph Anomaly Detection](https://mlsanity.com/paper/2306.12251/) (2023)
- [Graph Anomaly Detection via Multi-Scale Contrastive Learning Networks with Augmented View](https://mlsanity.com/paper/2212.00535/) (2022)
- [Node Dependent Local Smoothing for Scalable Graph Learning](https://mlsanity.com/paper/2110.14377/) (2021)
- [GAD-NR: Graph Anomaly Detection via Neighborhood Reconstruction](https://mlsanity.com/paper/2306.01951/) (2023)
- [Truncated Affinity Maximization: One-class Homophily Modeling for Graph Anomaly Detection](https://mlsanity.com/paper/2306.00006/) (2023)
- [Outlier Aware Network Embedding for Attributed Networks](https://mlsanity.com/paper/1811.07609/) (2018)
- [PREM: A Simple Yet Effective Approach for Node-Level Graph Anomaly Detection](https://mlsanity.com/paper/2310.11676/) (2023)
- [Rayleigh Quotient Graph Neural Networks for Graph-level Anomaly Detection](https://mlsanity.com/paper/2310.02861/) (2023)
- [Graph Neural Networks Exponentially Lose Expressive Power for Node Classification](https://mlsanity.com/paper/1905.10947/) (2019)
- [Unsupervised Graph Outlier Detection: Problem Revisit, New Insight, and Superior Method](https://mlsanity.com/paper/2210.12941/) (2022)
- [ARISE: Graph Anomaly Detection on Attributed Networks via Substructure Awareness](https://mlsanity.com/paper/2211.15255/) (2022)
- [Class Label-aware Graph Anomaly Detection](https://mlsanity.com/paper/2308.11669/) (2023)
- [Reinforcement Neighborhood Selection for Unsupervised Graph Anomaly Detection](https://mlsanity.com/paper/2312.05526/) (2023)
- [Normality Learning-based Graph Anomaly Detection via Multi-Scale Contrastive Learning](https://mlsanity.com/paper/2309.06034/) (2023)
- [Learning Based Proximity Matrix Factorization for Node Embedding](https://mlsanity.com/paper/2106.05476/) (2021)

## Built on by (most cited first, 11 of 11)

- [Decoupled Graph Energy-based Model for Node Out-of-Distribution Detection on Heterophilic Graphs](https://mlsanity.com/paper/2502.17912/) (2025)
- [Towards Anomaly Detection on Relational Data](https://mlsanity.com/paper/2606.18621/) (2026)
- [AC2L-GAD: Active Counterfactual Contrastive Learning for Graph Anomaly Detection](https://mlsanity.com/paper/2601.21171/) (2026)
- [Enhancing Spectral Graph Neural Networks with LLM-Predicted Homophily](https://mlsanity.com/paper/2506.14220/) (2025)
- [Combining Euclidean and Hyperbolic Representations for Node-level Anomaly Detection](https://mlsanity.com/paper/2510.11827/) (2025)
- [Mitigating Homophily Disparity in Graph Anomaly Detection: A Scalable and Adaptive Approach](https://mlsanity.com/paper/2603.08137/) (2026)
- [TA-GGAD: Testing-time Adaptive Graph Model for Generalist Graph Anomaly Detection](https://mlsanity.com/paper/2603.09349/) (2026)
- [TAS-GNN: A Status-Aware Signed Graph Neural Network for Anomaly Detection in Bitcoin Trust Systems](https://mlsanity.com/paper/2603.13290/) (2026)
- [NK-GAD: Neighbor Knowledge-Enhanced Unsupervised Graph Anomaly Detection](https://mlsanity.com/paper/2604.15668/) (2026)
- [GAD in the Wild: Benchmarking Graph Anomaly Detection under Realistic Deployment Challenges](https://mlsanity.com/paper/2605.07133/) (2026)
- [RagGAD: Rationale-Aware Conditional Gaussian Mixture Normalizing Flow for Unsupervised Graph Anomaly Detection](https://mlsanity.com/paper/2608.16018/) (2026)

## Abstract (arXiv)

The smoothing issue in graph learning leads to indistinguishable node representations, posing significant challenges for graph-related tasks. However, our experiments reveal that this problem can uncover underlying properties of node anomaly detection (NAD) that previous research has missed. We introduce Individual Smoothing Patterns (ISP) and Neighborhood Smoothing Patterns (NSP), which indicate that the representations of anomalous nodes are harder to smooth than those of normal ones. In addition, we explore the theoretical implications of these patterns, demonstrating the potential benefits of ISP and NSP for NAD tasks. Motivated by these findings, we propose SmoothGNN, a novel unsupervised NAD framework. First, we design a learning component to explicitly capture ISP for detecting node anomalies. Second, we design a spectral graph neural network to implicitly learn ISP to enhance detection. Third, we design an effective coefficient based on our findings that NSP can serve as coefficients for node representations, aiding in the identification of anomalous nodes. Furthermore, we devise a novel anomaly measure to calculate loss functions and anomalous scores for nodes, reflecting the properties of NAD using ISP and NSP. Extensive experiments on 9 real datasets show that SmoothGNN outperforms the best rival by an average of 14.66% in AUC and 7.28% in Average Precision, with 75x running time speedup, validating the effectiveness and efficiency of our framework.