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

Yunhui Liu; Qizhuo Xie; Yinfeng Chen; Xudong Jin; Tao Zheng; Bin Chong; Tieke He

cs.LGMar 9, 2026

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

Authors: Yunhui Liu, Qizhuo Xie, Yinfeng Chen, Xudong Jin, Tao Zheng, Bin Chong, Tieke He

Organizations: State Key Laboratory for Novel Software Technology, Nanjing University, Nanjing, China · National Engineering Laboratory for Big Data Analysis and Applications, Peking University, Beijing, China

Abstract

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.

Figures & tables

Panel of Figure 1 — Figure 1. (a), (b): Distribution of node homophily on Weibo and T-Finance. (c), (d): Performance disparity across node homophily quartiles (Q1 = top 25% homophily, Q4 = bottom 25%) on Weibo and T-Finance.

Figure 2. Overview of our proposed SAGAD. It consists of three main designs: 1) Dual-pass Chebyshev Polynomial Filter extracts both low- and high-frequency embeddings to capture homophilic and heterophilic patterns; 2) Anomaly Context-aware Adaptive Fusion dynamically integrates these embeddings based on node-specific structural contexts; 3) Frequency Preference Guidance Loss regularizes fusion weights to align with class-specific spectral preferences, enhancing anomaly discrimination.

Model	Reddit	Weibo	Amazon	Yelp.	T-Fin.	Ellip.	Tolo.	Quest.	DGraph.	T-Social	Avg.
GCN	4.2±0.8	86.0±6.7	32.8±1.2	16.4±2.6	60.5±10.8	43.1±4.6	33.0±3.6	6.1±0.9	2.3±0.2	8.4±3.8	29.3
GIN	4.3±0.6	67.6±7.4	75.4±4.3	23.7±5.4	44.8±7.1	40.1±3.2	31.8±3.2	6.7±1.1	2.0±0.1	6.2±1.7	30.3
SAGE	4.5±0.6	58.5±6.2	42.5±6.1	20.9±3.5	11.7±5.2	43.1±5.6	34.0±2.1	5.5±1.3	2.0±0.2	7.8±1.3	23.0
GAT	4.7±0.7	73.3±7.3	81.6±1.7	25.0±2.9	28.9±8.6	44.2±6.6	33.0±2.0	7.3±1.2	2.2±0.2	9.2±2.0	30.9
H2GCN	4.6±0.7	76.5±5.8	80.9±2.6	24.4±3.7	34.2±10.1	46.8±8.1	33.6±2.2	7.4±1.3	2.4±0.3	10.4±1.9	32.1
ACM	4.4±0.7	66.0±8.7	54.0±19.0	21.4±2.7	29.2±16.8	55.1±4.8	34.4±3.5	7.2±1.9	2.2±0.4	6.0±1.6	28.0

Table 1. Comparison of AUPRC for each model. "-" denotes "out of memory".

Dataset	Weibo			T-Finance			Amazon			YelpChi
Dataset	Q1-Q2	Q1-Q3	Q1-Q4	Q1-Q2	Q1-Q3	Q1-Q4	Q1-Q2	Q1-Q3	Q1-Q4	Q1-Q2	Q1-Q3	Q1-Q4
AMNet	9.40	32.88	27.32	3.44	30.27	58.66	5.43	20.65	47.10	-0.71	-0.19	0.54
BWGNN	10.73	39.18	44.89	9.47	56.56	86.60	8.89	26.14	56.74	-1.09	-0.60	0.43
ConsisGAD	13.43	43.95	54.96	3.75	25.04	89.25	-3.24	14.63	39.47	-1.75	-0.19	-0.06
SAGAD	1.95	7.37	35.26	1.46	26.26	70.22	5.42	14.95	46.93	4.30	6.25	7.07

Table 2. Performance gaps (AUPRC difference) between Q1 and other quartiles across datasets. Lower absolute values indicate smaller homophily disparity.

Panel of Figure 3 — Figure 3. Performance disparity across node homophily quartiles (Q1 = top 25% homophily, Q4 = bottom 25%) on Amazon and YelpChi.

Model	YelpChi		T-Social
Model	Time (s)	Mem. (MB)	Time (s)	Mem. (MB)
GCN	1.93	547.73	61.75	13241.26
AMNet	4.09	773.38	213.82	18970.04
BWGNN	2.66	729.17	112.01	16146.46
GHRN	3.22	3360.71	161.00	28080.33
ConsisGAD	89.28	16390.42	1674.87	14145.61

Table 3. Scalability comparison in terms of training time and GPU memory.

$\boldsymbol{Z}_{L}$	$\boldsymbol{Z}_{H}$	$\mathcal{G}^{RQ}$	$\mathcal{L}_{fpg}$	Fusion	Reddit		Amazon		Yelp.		T-Fin.		Ellip.		Tolo.		DGraph.
$\boldsymbol{Z}_{L}$	$\boldsymbol{Z}_{H}$	$\mathcal{G}^{RQ}$	$\mathcal{L}_{fpg}$	Fusion	AUPRC	AUROC	AUPRC	AUROC	AUPRC	AUROC	AUPRC	AUROC	AUPRC	AUROC	AUPRC	AUROC	AUPRC	AUROC
✓	✓	✓	✓	Eq. (7)	5.6±0.6	66.5±3.0	84.7±2.0	94.5±2.1	27.8±2.4	68.8±2.5	82.8±1.0	94.4±0.4	57.1±4.1	90.9±0.9	40.5±1.6	73.6±0.8	2.6±0.3	70.8±1.9
✓	✓	✓	✗	Eq. (7)	5.3±0.7	63.9±3.6	83.8±2.4	94.3±1.9	26.6±1.7	68.1±2.5	78.1±6.1	93.2±2.1	56.6±6.0	90.5±1.1	35.0±2.0	69.1±1.8	2.3±0.2	69.6±1.3
✓	✓	✢	✓	Eq. (7)	5.5±0.7	65.6±2.9	83.0±2.3	93.8±2.0	23.1±2.8	63.9±4.3	78.1±4.3	93.2±1.3	51.9±3.9	90.1±1.2	33.7±1.3	68.2±1.7	2.2±0.2	69.0±1.3
✓	✓	✗	✓	Eq. (7)	5.2±0.7	63.8±3.7	83.2±2.0	93.9±2.1	23.1±2.8	63.8±4.3	79.1±3.6	93.3±1.3	51.7±3.3	90.2±1.2	34.0±1.4	68.8±1.2	2.2±0.2	69.1±1.5
✓	✓	✗	✗	Mean	5.1±0.7	66.0±2.4	82.3±3.3	93.9±2.0	23.1±3.0	64.1±4.8	67.1±0.9	88.2±1.3	52.5±3.8	90.4±0.7	33.2±1.2	68.3±1.4	2.2±0.2	68.8±1.4

Table 4. Ablation study on each component of our SAGAD in terms of AUPRC and AUROC.

Panel of Figure 4 — Figure 4. Visualization of the learned coefficients for the top 8 dimensions. Nodes ( $a_{1},a_{2},a_{3}$ ) and ( $n_{1},n_{2},n_{3}$ ) are randomly selected abnormal and normal nodes, respectively.

Dataset	#Nodes	#Edges	#Feat.	Anomaly	$h$	$h^{a}$	$h^{n}$	Relation Concept	Feature Type
Reddit	10,984	168,016	64	3.3%	0.947	0.000	0.994	Under Same Post	Text Embedding
Weibo	8,405	407,963	400	10.3%	0.977	0.858	0.977	Under Same Hashtag	Text Embedding
Amazon	11,944	4,398,392	25	9.5%	0.954	0.102	0.968	Review Correlation	Misc. Information
YelpChi	45,954	3,846,979	32	14.5%	0.773	0.195	0.867	Reviewer Interaction	Misc. Information
T-Finance	39,357	21,222,543	10	4.6%	0.971	0.543	0.976	Transaction Record	Misc. Information
Elliptic	203,769	234,355	166	9.8%	0.970	0.234	0.985	Payment Flow	Misc. Information

Table 5. Dataset statistics including the number of nodes and edges, the node feature dimension, the ratio of anomalies, the homophily ratio, the concept of relations, and the type of node features.

h

h^{a}

, and

h^{n}

represent the edge homophily, the average homophily for abnormal nodes, and the average homophily for normal nodes, respectively. As we can see,

h^{a}

is much smaller than

h^{n}

, indicating that abnormal nodes exhibit significantly lower homophily compared to normal nodes. "Misc." refers to node features that are heterogeneous attributes, which may include categorical, numerical, and temporal information.

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Panel of Figure 5 — Figure 5. How the AUPRC score varies with different values of $p_{a}$ and $p_{n}$ .

Model	Reddit	Weibo	Amazon	Yelp.	T-Fin.	Ellip.	Tolo.	Quest.	DGraph.	T-Social	Avg.
GCN	56.9±5.9	93.5±6.6	82.0±0.3	51.2±3.7	88.3±2.5	86.2±1.9	64.2±4.8	60.0±2.2	66.2±2.5	71.6±10.4	72.0
GIN	60.0±4.1	83.8±8.3	91.6±1.7	62.9±7.3	84.5±4.5	88.2±0.9	66.8±5.2	62.2±2.2	65.7±1.8	70.4±7.4	73.6
SAGE	60.3±3.8	81.8±6.5	81.4±2.0	58.9±4.3	68.9±5.5	87.4±1.0	67.6±4.2	61.2±2.9	64.8±3.3	72.0±2.9	70.4
GAT	60.5±3.9	86.4±7.7	92.4±1.9	65.6±4.0	85.0±4.5	88.5±2.1	68.1±3.0	62.3±1.4	67.2±1.9	75.4±4.8	75.1
H2GCN	60.3±4.4	87.8±5.7	91.4±2.4	65.0±4.5	86.3±3.9	89.3±2.1	69.1±2.5	61.9±4.2	69.0±1.9	74.5±3.7	75.5
ACM	60.0±4.3	92.5±2.9	81.8±7.9	61.3±3.8	82.2±8.1	90.0±0.8	69.3±4.2	60.8±4.1	67.6±5.3	68.3±4.9	73.3

Appendix

Table 6. Comparison of AUROC for each model. "-" denotes "out of memory".

Model	Reddit	Weibo	Amazon	Yelp.	T-Fin.	Ellip.	Tolo.	Quest.	DGraph.	T-Social	Avg.
GCN	6.2±2.2	79.2±4.3	36.9±2.6	16.9±3.0	60.6±7.6	49.7±4.2	33.4±3.5	9.8±1.2	3.6±0.4	10.2±8.1	30.6
GIN	4.8±1.9	66.5±7.3	70.4±5.7	26.5±6.1	54.4±5.0	47.6±3.1	33.6±3.0	10.3±1.1	2.1±0.5	5.3±2.9	32.2
SAGE	5.8±0.8	63.4±6.0	48.0±5.6	22.9±3.6	18.5±9.4	48.2±5.8	35.2±2.2	8.8±2.5	2.5±0.7	9.5±2.9	26.3
GAT	6.5±2.3	70.2±4.6	77.1±1.7	28.1±3.4	36.2±10.3	51.4±5.8	35.1±1.8	10.9±0.9	3.1±0.7	11.6±3.0	33.0
H2GCN	5.8±2.2	71.1±4.9	77.5±2.5	27.2±4.2	43.6±11.7	53.9±6.9	35.2±2.0	11.2±1.9	3.4±0.9	14.9±2.9	34.4
ACM	5.4±1.8	70.7±9.5	56.1±14.2	23.9±3.8	37.2±19.3	55.2±3.3	35.8±4.2	11.4±2.6	1.9±0.7	8.1±1.8	30.6

Appendix

Table 7. Comparison of Rec@K for each model. "-" denotes "out of memory".

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Graph anomaly detection aims to identify nodes that deviate from normal behavioral patterns within graphs. However, existing methods largely rely on the homophily assumption, which makes it difficult to distinguish spurious affinities and to capture the diverse behaviors of normal nodes,limiting their robustness in complex real-world scenarios. To address this problem, we propose RagGAD, an unsupervised graph anomaly detection framework based on rationale-aware conditional Gaussian mixture normalizing flow. RagGAD introduces an adaptive rationale disentangler to disentangle stable rationales from spurious correlations within node interrelationships, and further decomposes stable rationales into robust and fragile components. The learned rationales capture underlying interaction patterns that characterize normal behaviors under varying conditions, while anomalies emerge as deviations associated with unstable or spurious correlations. To model the intricate distributions of normal and abnormal nodes, RagGAD integrates rationale-non-rationale Gaussian mixture modeling with a robust-fragile rationale mixture learning strategy. By mitigating spurious homophilic correlations and embracing the heterogeneity of normal patterns, RagGAD identifies anomalies as low-density regions within a structure-aware distribution space. Extensive experiments on multiple benchmark datasets demonstrate that RagGAD outperforms state-of-the-art methods.

Abstract

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