# Addressing Graph Anomaly Detection via Causal Edge Separation and Spectrum

arXiv: https://arxiv.org/abs/2508.14684 · HTML: https://mlsanity.com/paper/2508.14684/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 23 references that are in the map.
- First posted on arXiv 20 Aug 2025.

## Builds on (most cited first, 14 of 14)

- [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)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (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)
- [Node Similarity Preserving Graph Convolutional Networks](https://mlsanity.com/paper/2011.09643/) (2020)
- [From Amateurs to Connoisseurs: Modeling the Evolution of User Expertise through Online Reviews](https://mlsanity.com/paper/1303.4402/) (2013)
- [Non-Local Graph Neural Networks](https://mlsanity.com/paper/2005.14612/) (2020)
- [Alleviating the Inconsistency Problem of Applying Graph Neural Network to Fraud Detection](https://mlsanity.com/paper/2005.00625/) (2020)
- [Alleviating Structural Distribution Shift in Graph Anomaly Detection](https://mlsanity.com/paper/2401.14155/) (2024)
- [Label Information Enhanced Fraud Detection against Low Homophily in Graphs](https://mlsanity.com/paper/2302.10407/) (2023)

## Abstract (arXiv)

In the real world, anomalous entities often add more legitimate connections while hiding direct links with other anomalous entities, leading to heterophilic structures in anomalous networks that most GNN-based techniques fail to address. Several works have been proposed to tackle this issue in the spatial domain. However, these methods overlook the complex relationships between node structure encoding, node features, and their contextual environment and rely on principled guidance, research on solving spectral domain heterophilic problems remains limited. This study analyzes the spectral distribution of nodes with different heterophilic degrees and discovers that the heterophily of anomalous nodes causes the spectral energy to shift from low to high frequencies. To address the above challenges, we propose a spectral neural network CES2-GAD based on causal edge separation for anomaly detection on heterophilic graphs. Firstly, CES2-GAD will separate the original graph into homophilic and heterophilic edges using causal interventions. Subsequently, various hybrid-spectrum filters are used to capture signals from the segmented graphs. Finally, representations from multiple signals are concatenated and input into a classifier to predict anomalies. Extensive experiments with real-world datasets have proven the effectiveness of the method we proposed.