# Robust Anomaly Detection with Graph Neural Networks using Controllability

arXiv: https://arxiv.org/abs/2507.13954 · HTML: https://mlsanity.com/paper/2507.13954/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 29 references that are in the map.
- First posted on arXiv 18 Jul 2025.

## Builds on (most cited first, 22 of 22)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [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 Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [How Attentive are Graph Attention Networks?](https://mlsanity.com/paper/2105.14491/) (2021)
- [Masked Label Prediction: Unified Message Passing Model for Semi-Supervised Classification](https://mlsanity.com/paper/2009.03509/) (2020)
- [Residual Gated Graph ConvNets](https://mlsanity.com/paper/1711.07553/) (2017)
- [DeeperGCN: All You Need to Train Deeper GCNs](https://mlsanity.com/paper/2006.07739/) (2020)
- [A Comprehensive Survey on Graph Anomaly Detection with Deep Learning](https://mlsanity.com/paper/2106.07178/) (2021)
- [Topology Adaptive Graph Convolutional Networks](https://mlsanity.com/paper/1710.10370/) (2017)
- [GADBench: Revisiting and Benchmarking Supervised Graph Anomaly Detection](https://mlsanity.com/paper/2306.12251/) (2023)
- [GAD-NR: Graph Anomaly Detection via Neighborhood Reconstruction](https://mlsanity.com/paper/2306.01951/) (2023)
- [Boost then Convolve: Gradient Boosting Meets Graph Neural Networks](https://mlsanity.com/paper/2101.08543/) (2021)
- [PREM: A Simple Yet Effective Approach for Node-Level Graph Anomaly Detection](https://mlsanity.com/paper/2310.11676/) (2023)
- [Graph Anomaly Detection with Graph Neural Networks: Current Status and Challenges](https://mlsanity.com/paper/2209.14930/) (2022)
- [ADA-GAD: Anomaly-Denoised Autoencoders for Graph Anomaly Detection](https://mlsanity.com/paper/2312.14535/) (2023)
- [Graph-level Anomaly Detection via Hierarchical Memory Networks](https://mlsanity.com/paper/2307.00755/) (2023)
- [Class Label-aware Graph Anomaly Detection](https://mlsanity.com/paper/2308.11669/) (2023)
- [Improving Graph Machine Learning Performance Through Feature Augmentation Based on Network Control Theory](https://mlsanity.com/paper/2405.03706/) (2024)
- [Multi-representations Space Separation based Graph-level Anomaly-aware Detection](https://mlsanity.com/paper/2307.12994/) (2023)

## Abstract (arXiv)

Anomaly detection in complex domains poses significant challenges due to the need for extensive labeled data and the inherently imbalanced nature of anomalous versus benign samples. Graph-based machine learning models have emerged as a promising solution that combines attribute and relational data to uncover intricate patterns. However, the scarcity of anomalous data exacerbates the challenge, which requires innovative strategies to enhance model learning with limited information. In this paper, we hypothesize that the incorporation of the influence of the nodes, quantified through average controllability, can significantly improve the performance of anomaly detection. We propose two novel approaches to integrate average controllability into graph-based frameworks: (1) using average controllability as an edge weight and (2) encoding it as a one-hot edge attribute vector. Through rigorous evaluation on real-world and synthetic networks with six state-of-the-art baselines, our proposed methods demonstrate improved performance in identifying anomalies, highlighting the critical role of controllability measures in enhancing the performance of graph machine learning models. This work underscores the potential of integrating average controllability as additional metrics to address the challenges of anomaly detection in sparse and imbalanced datasets.