# Mitigating Homophily Disparity in Graph Anomaly Detection: A Scalable and Adaptive Approach

arXiv: https://arxiv.org/abs/2603.08137 · HTML: https://mlsanity.com/paper/2603.08137/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 46 references that are in the map.
- First posted on arXiv 9 Mar 2026.

## Builds on (most cited first, 25 of 25)

- [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)
- [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)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Predicting Dynamic Embedding Trajectory in Temporal Interaction Networks](https://mlsanity.com/paper/1908.01207/) (2019)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [Enhancing Graph Neural Network-based Fraud Detectors against Camouflaged Fraudsters](https://mlsanity.com/paper/2008.08692/) (2020)
- [BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation](https://mlsanity.com/paper/2106.10994/) (2021)
- [Rethinking Graph Neural Networks for Anomaly Detection](https://mlsanity.com/paper/2205.15508/) (2022)
- [Anomaly Detection on Attributed Networks via Contrastive Self-Supervised Learning](https://mlsanity.com/paper/2103.00113/) (2021)
- [Revisiting Heterophily For Graph Neural Networks](https://mlsanity.com/paper/2210.07606/) (2022)
- [Contextual Stochastic Block Models](https://mlsanity.com/paper/1807.09596/) (2018)
- [Consistency of spectral clustering in stochastic block models](https://mlsanity.com/paper/1312.2050/) (2013)
- [From Amateurs to Connoisseurs: Modeling the Evolution of User Expertise through Online Reviews](https://mlsanity.com/paper/1303.4402/) (2013)
- [Convolutional Neural Networks on Graphs with Chebyshev Approximation, Revisited](https://mlsanity.com/paper/2202.03580/) (2022)
- [Graph Convolution for Semi-Supervised Classification: Improved Linear Separability and Out-of-Distribution Generalization](https://mlsanity.com/paper/2102.06966/) (2021)
- [GADBench: Revisiting and Benchmarking Supervised Graph Anomaly Detection](https://mlsanity.com/paper/2306.12251/) (2023)
- [Spam Review Detection with Graph Convolutional Networks](https://mlsanity.com/paper/1908.10679/) (2019)
- [AdaGNN: Graph Neural Networks with Adaptive Frequency Response Filter](https://mlsanity.com/paper/2104.12840/) (2021)
- [Node-wise Filtering in Graph Neural Networks: A Mixture of Experts Approach](https://mlsanity.com/paper/2406.03464/) (2024)
- [SpaceGNN: Multi-Space Graph Neural Network for Node Anomaly Detection with Extremely Limited Labels](https://mlsanity.com/paper/2502.03201/) (2025)
- [SmoothGNN: Smoothing-aware GNN for Unsupervised Node Anomaly Detection](https://mlsanity.com/paper/2405.17525/) (2024)
- [Learning Accurate, Efficient, and Interpretable MLPs on Multiplex Graphs via Node-wise Multi-View Ensemble Distillation](https://mlsanity.com/paper/2502.05864/) (2025)

## Abstract (arXiv)

Graph anomaly detection (GAD) aims to identify nodes that deviate from normal patterns in structure or features. While recent GNN-based approaches have advanced this task, they struggle with two major challenges: 1) homophily disparity, where nodes exhibit varying homophily at both class and node levels; and 2) limited scalability, as many methods rely on costly whole-graph operations. To address them, we propose SAGAD, a Scalable and Adaptive framework for GAD. SAGAD precomputes multi-hop embeddings and applies reparameterized Chebyshev filters to extract low- and high-frequency information, enabling efficient training and capturing both homophilic and heterophilic patterns. To mitigate node-level homophily disparity, we introduce an Anomaly Context-Aware Adaptive Fusion, which adaptively fuses low- and high-pass embeddings using fusion coefficients conditioned on Rayleigh Quotient-guided anomalous subgraph structures for each node. To alleviate class-level disparity, we design a Frequency Preference Guidance Loss, which encourages anomalies to preserve more high-frequency information than normal nodes. SAGAD supports mini-batch training, achieves linear time and space complexity, and drastically reduces memory usage on large-scale graphs. Theoretically, SAGAD ensures asymptotic linear separability between normal and abnormal nodes under mild conditions. Extensive experiments on 10 benchmarks confirm SAGAD's superior accuracy and scalability over state-of-the-art methods.