Graph neural network node classification model incorporating clustering coefficients

doi:10.11772/j.issn.1001-9081.2025060793

Journal of Computer Applications ›› 2026, Vol. 46 ›› Issue (6): 1855-1862.DOI: 10.11772/j.issn.1001-9081.2025060793

• Data science and technology • Previous Articles

Graph neural network node classification model incorporating clustering coefficients

Yasong ZHANG¹, Bihui CONG², Shuang XU¹()

^1.College of Information and Communication Engineering，Dalian Minzu University，Dalian Liaoning 116600，China
^2.Academy of the Zhonghuaminzu Community，Dalian Minzu University，Dalian Liaoning 116600，China

Received:2025-07-17 Revised:2025-09-20 Accepted:2025-09-25 Online:2025-10-16 Published:2026-06-10
Contact: Shuang XU
About author:ZHANG Yasong， born in 2001， M. S. candidate. Her research interests include node classification， attention mechanism.
CONG Bihui， born in 1989， Ph. D. candidate， lecturer. Her research interests include communication studies.
First author contact:XU Shuang， born in 1978， Ph. D.， professor. Her research interests include big data analysis and processing of complex network.
Supported by:
Research Project on Humanities and Social Sciences by the Ministry of Education in 2023(23YJCZH028);Fundamental Research Funds for the Central Universities(044420250008)

引入聚类系数的图神经网络节点分类模型

张雅淞¹, 丛碧辉², 许爽¹()

^1.大连民族大学信息与通信工程学院，辽宁大连 116600
^2.大连民族大学中华民族共同体研究院，辽宁大连 116600

通讯作者: 许爽
作者简介:张雅淞（2001—），女，辽宁阜新人，硕士研究生，CCF会员，主要研究方向：节点分类、注意力机制
丛碧辉（1989—），女，吉林四平人，讲师，博士研究生，主要研究方向：传播学
第一联系人：许爽（1978—），女，辽宁大连人，教授，博士，主要研究方向：复杂网络的大数据分析与处理。
基金资助:
2023年度教育部人文社会科学研究项目(23YJCZH028);中央高校基本科研业务费专项资金资助项目(044420250008)

Abstract

Abstract:

To address the issues of structural unfairness and classification inaccuracy of Graph ATtention network （GAT） model in node classification tasks， a Graph Neural Network （GNN） node classification model incorporating clustering coefficients， named GATcc（GAT with clustering coefficient）， was proposed. Firstly， by introducing the clustering coefficients of neighboring nodes as structural information， and combining trainable weight parameters， the representation ability of the topological structure in the attention mechanism was enhanced. Then， feature scaling was employed to optimize node embeddings， and residual connections were added to mitigate the risk of feature over-smoothing. Experimental results on six real datasets demonstrate that the proposed model outperforms the mainstream models， such as Graph Isomorphism Network （GIN） and GOAT （Graph Ordering Attention Network）， in classification accuracy. For instance， compared to the baseline model GAT on the Cora dataset， the proposed model has the classification accuracy improved by 4.03 percentage points， the structural bias reduced from 0.31% to 0.11%， and the classification accuracy of isolated nodes improved by 3.69 percentage points. In conclusion， the proposed model not only achieves significant improvements in classification performance， but also shows superiority in structural fairness and stability.

Key words: node classification, attention mechanism, clustering coefficient, topological information, structural fairness

摘要：

针对图注意力网络（GAT）模型在节点分类任务中存在的结构不公平性和分类不准确问题，提出一种引入聚类系数的图神经网络（GNN）节点分类模型GATcc（GAT with clustering coefficient）。首先，通过引入邻居节点的聚类系数作为结构信息，结合可训练的权重参数，增强拓扑结构在注意力机制中的表达能力；其次，采用特征缩放优化节点嵌入，并加入残差连接以减轻特征过平滑的风险。在6个真实数据集上的实验结果表明，该模型的分类准确率超过图同构网络（GIN）和GOAT（Graph Ordering Attention Network）等主流模型。例如，相较于基线模型GAT，所提模型的分类准确率在Cora数据集上提升了4.03个百分点，结构性偏差从0.31%降低到0.11%，而孤立节点的分类准确率提升了3.69个百分点。综上，所提模型不仅在分类性能上取得了显著提升，还在结构公平性与稳定性方面展现出优越性。

关键词: 节点分类, 注意力机制, 聚类系数, 拓扑信息, 结构公平性

CLC Number:

TP183

Yasong ZHANG, Bihui CONG, Shuang XU. Graph neural network node classification model incorporating clustering coefficients[J]. Journal of Computer Applications, 2026, 46(6): 1855-1862.

张雅淞, 丛碧辉, 许爽. 引入聚类系数的图神经网络节点分类模型[J]. 《计算机应用》唯一官方网站, 2026, 46(6): 1855-1862.

Figures/Tables 10

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数据集	节点数	边数	类别数	特征维度
Cora	2 708	5 429	7	1 433
CiteSeer	3 312	4 732	6	3 703
PubMed	19 717	44 338	3	500
Wiki-CS	11 701	431 726	10	767
AMZ-photo	7 487	245 812	745	8
AMZ-computers	13 752	491 722	10	300

数据集	节点数	边数	类别数	特征维度
Cora	2 708	5 429	7	1 433
CiteSeer	3 312	4 732	6	3 703
PubMed	19 717	44 338	3	500
Wiki-CS	11 701	431 726	10	767
AMZ-photo	7 487	245 812	745	8
AMZ-computers	13 752	491 722	10	300

保留百分比/%	Cora			CiteSeer			PubMed
保留百分比/%	Acc/%	F1/%	Time/s	Acc/%	F1/%	Time/s	Acc/%	F1/%	Time/s
50	81.08	79.37	64	68.17	61.42	75	75.36	75.01	102
70	87.15	86.22	77	69.88	66.26	100	78.65	78.33	165
90	84.48	83.93	97	66.61	65.28	122	80.96	79.74	256
100	86.68	85.77	116	68.80	65.58	210	79.83	79.54	621
保留百分比/%	Wiki-CS			AMZ-photo			AMZ-computers
保留百分比/%	Acc/%	F1/%	Time/s	Acc/%	F1/%	Time/s	Acc/%	F1/%	Time/s
50	93.78	91.49	111	91.63	86.28	117	85.27	77.83	114
70	92.75	90.30	87	92.53	90.21	145	85.79	78.26	101
90	92.82	90.86	137	94.48	93.44	137	86.79	79.94	158
100	92.16	90.31	159	94.44	92.52	259	85.33	75.19	224

保留百分比/%	Cora			CiteSeer			PubMed
保留百分比/%	Acc/%	F1/%	Time/s	Acc/%	F1/%	Time/s	Acc/%	F1/%	Time/s
50	81.08	79.37	64	68.17	61.42	75	75.36	75.01	102
70	87.15	86.22	77	69.88	66.26	100	78.65	78.33	165
90	84.48	83.93	97	66.61	65.28	122	80.96	79.74	256
100	86.68	85.77	116	68.80	65.58	210	79.83	79.54	621
保留百分比/%	Wiki-CS			AMZ-photo			AMZ-computers
保留百分比/%	Acc/%	F1/%	Time/s	Acc/%	F1/%	Time/s	Acc/%	F1/%	Time/s
50	93.78	91.49	111	91.63	86.28	117	85.27	77.83	114
70	92.75	90.30	87	92.53	90.21	145	85.79	78.26	101
90	92.82	90.86	137	94.48	93.44	137	86.79	79.94	158
100	92.16	90.31	159	94.44	92.52	259	85.33	75.19	224

模型	Cora		CiteSeer		PubMed		Wiki-CS		AMZ-photo		AMZ-computers
模型	Acc	F1	Acc	F1	Acc	F1	Acc	F1	Acc	F1	Acc	F1
GCN	76.68	76.41	64.25	65.07	76.20	76.12	83.95	81.25	75.94	74.21	66.64	60.73
Tail-GNN	81.44	80.48	67.30	61.32	76.30	75.93	90.45	90.05	90.32	88.93	85.23	76.30
GOAT	83.13	82.36	67.85	65.28	78.81	77.37	90.81	89.40	92.85	91.65	82.74	72.55
NodeFormer	82.28	81.58	67.55	66.91	78.65	77.36	91.92	90.24	93.13	92.62	79.11	68.33
SGFormer	84.53	83.74	67.91	65.63	78.98	77.48	91.73	90.62	94.24	92.84	83.40	72.11
GIN	84.23	83.93	67.34	66.03	78.23	77.84	91.84	90.21	94.26	93.30	85.04	75.01
GAT	82.65	82.83	67.46	63.24	77.43	76.65	90.55	90.11	93.44	92.95	82.55	71.75
GATcc	86.68	85.77	68.80	65.51	79.83	79.54	92.16	91.74	94.48	93.38	86.43	77.66

Graph neural network node classification model incorporating clustering coefficients

引入聚类系数的图神经网络节点分类模型

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Figures/Tables 10

References 27

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Metrics

模型	Cora		AMZ-photo
模型	MSE	RMSE	MSE	RMSE
GAT	0.009 0	0.094 8	0.013 9	0.117 9
GOAT	0.007 8	0.088 3	0.003 2	0.056 6
GIN	0.007 2	0.084 9	0.015 0	0.122 5
GATcc	0.006 4	0.080 1	0.002 1	0.045 8

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数据集	聚类系数	残差连接	特征缩放	Acc	F1
Cora	√	√	√	86.68	85.77
		√	√	84.63	83.95
	√		√	85.80	85.02
	√	√		86.12	85.33
CiteSeer	√	√	√	68.80	65.51
		√	√	66.48	63.20
	√		√	67.91	64.73
	√	√		68.02	64.63
AMZ-photo	√	√	√	94.48	93.38
		√	√	92.82	91.90
	√		√	93.55	92.32
	√	√		93.93	92.57
AMZ-computers	√	√	√	86.43	77.66
		√	√	84.72	76.83
	√		√	85.84	77.04
	√	√		86.16	77.58

数据集	聚类系数	残差连接	特征缩放	Acc	F1
Cora	√	√	√	86.68	85.77
		√	√	84.63	83.95
	√		√	85.80	85.02
	√	√		86.12	85.33
CiteSeer	√	√	√	68.80	65.51
		√	√	66.48	63.20
	√		√	67.91	64.73
	√	√		68.02	64.63
AMZ-photo	√	√	√	94.48	93.38
		√	√	92.82	91.90
	√		√	93.55	92.32
	√	√		93.93	92.57
AMZ-computers	√	√	√	86.43	77.66
		√	√	84.72	76.83
	√		√	85.84	77.04
	√	√		86.16	77.58