---
title: "Graph neural network (graph convolution)"
description: "Graph neural network (graph convolution) was mentioned in 110 papers in the last 30 days (2026-09-27 to 2026-10-26), ranking #8 of the 104 equations and models mentioned."
url: https://scholar4ai.com/equations/graph-neural-network-graph-convolution
markdown_url: https://scholar4ai.com/equations/graph-neural-network-graph-convolution.md
license: CC BY-NC 4.0 (https://creativecommons.org/licenses/by-nc/4.0/)
data_url: https://scholar4ai.com/data/rankings.json
updated: 2026-10-26T13:22:50+09:00
window: 2026-09-27 to 2026-10-26
source: OpenAlex (CC0)
---

# Graph neural network (graph convolution)

$$
H^{(l+1)} = \sigma\big(\tilde D^{-1/2} \tilde A\, \tilde D^{-1/2} H^{(l)} W^{(l)}\big)
$$

Updates each node's representation from its neighbours' representations.

- area: Machine learning
- 8 papers in the last 7 days
- Names searched for: graph neural network, graph convolutional network, graph convolution, graph attention network, GCN, GNN

Back to the ranking: https://scholar4ai.com/rankings/equations.md

## Key findings

- Graph neural network (graph convolution) was mentioned in 110 papers in the last 30 days (2026-09-27 to 2026-10-26), ranking #8 of the 104 equations and models mentioned.
- By journal category: AI (99), Operations Research (5), Management (4) and Finance (2).
- Most of them appeared in Expert Systems with Applications (25), Pattern Recognition (23) and Applied Intelligence (8).
- Often mentioned together with Scaled dot-product attention (Transformer) (33), Convolutional neural network (CNN) (22) and Long short-term memory (LSTM) (19).
- Datasets named in the same papers: OR-Library (9), Twitter / X (4) and GLUE / SuperGLUE (3).
- From Apr 2024 to Sep 2026, 2,070 archived papers mentioned Graph neural network (graph convolution) in their title, abstract or keywords, most of them in May 2025 (130).

## Mentions over 30 months

*Papers mentioning it by publication month, Apr 2024 to Sep 2026 (titles, abstracts and keywords)*

| Trend | Apr 24–Sep 24 | Oct 24–Sep 25 | Oct 25–Sep 26 | 30 months |
|---|---:|---:|---:|---:|
|  | 520 | 1,269 | 281 | 2,070 |

*Papers mentioning Graph neural network (graph convolution), newest first. Newest 50 of 110 papers; all of them are in /data/papers.json.*

| Date | Title | Journal | Authors | Affiliations |
|---|---|---|---|---|
| 2026-10-24 | [A priority-aware dual-channel feature fusion method for urban rail service traffic classification](https://doi.org/10.1007/s10489-026-07560-z) | [Applied Intelligence](https://scholar4ai.com/journals/applied-intelligence.md) | Xinpeng Liu, Junhui Zhao, Zhengyuan Wu et al. | Beijing Jiaotong University |
| 2026-10-23 | [Efficient equivariant framework for universal charge density prediction](https://doi.org/10.1038/s42256-026-01326-5) | [Nature Machine Intelligence](https://scholar4ai.com/journals/nature-machine-intelligence.md) | Xiwen Li, Zaizhou Xin, Hongyu Yu et al. | Fudan University; State Key Laboratory of Surface Physics |
| 2026-10-22 | [Research on the spatiotemporal prediction of supply chain finance risk contagion based on a dynamic graph attention diffusion mechanism](https://doi.org/10.1186/s40854-026-00980-3) | [Financial Innovation](https://scholar4ai.com/journals/financial-innovation.md) | Yulong Zhang, Yulong Zhang, Yaqing Zhang et al. | Hengshui University; Columbia University |
| 2026-10-22 | [Beyond the survey: a systematic empirical study of detection and association in visual MOT](https://doi.org/10.1007/s10462-026-11713-4) | [Artificial Intelligence Review](https://scholar4ai.com/journals/artificial-intelligence-review.md) | Linh Van Ma, Juhua Hu, Wei Cheng et al. | Gwangju Institute of Science and Technology; University of Washington Tacoma |
| 2026-10-21 | [Quantum heterogeneous graph attention network](https://doi.org/10.1016/j.patcog.2026.115127) | [Pattern Recognition](https://scholar4ai.com/journals/pattern-recognition.md) | Wenjie Liu, Bohan Du, Qingshan Wu | Nanjing University of Information Science and Technology |
| 2026-10-21 | [VOGUE: Sequence-adaptive online graph tracking with virtual long-term memory](https://doi.org/10.1016/j.patcog.2026.115166) | [Pattern Recognition](https://scholar4ai.com/journals/pattern-recognition.md) | Yuhao Wei, Shoudong Han, Wenbo Zheng et al. | Huazhong University of Science and Technology |
| 2026-10-21 | [GCN-neural ODE-based diverging conflict resolution for ACT platoons: A case study of gap patterns on port collector-distributor highway](https://doi.org/10.1016/j.eswa.2026.134843) | [Expert Systems with Applications](https://scholar4ai.com/journals/expert-systems-with-applications.md) | Yi Li, Xin Chen, Weili Wang et al. | Tongji University; Shanghai Maritime University; Merchants Chongqing Communications Research and Design Institute; … |
| 2026-10-20 | [Forecast-guided multi-task scheduling for autonomous electric ride-hailing fleets under charging and maintenance constraints](https://doi.org/10.1016/j.eswa.2026.134759) | [Expert Systems with Applications](https://scholar4ai.com/journals/expert-systems-with-applications.md) | Yuhan Guo, Hongao Wang, Haoran Wang et al. | Zhejiang University of Science and Technology; Université d'Artois; United Arab Emirates University; … |
| 2026-10-19 | [MASIG: Multi-view augmentation for graph representation learning on structurally imbalanced graphs](https://doi.org/10.1016/j.eswa.2026.134763) | [Expert Systems with Applications](https://scholar4ai.com/journals/expert-systems-with-applications.md) | Bingqian Xue, Mingxia Zhao, S. H. Zhang et al. | China Agricultural University; Shanxi Science and Technology Department; Taiyuan University of Science and Technology |
| 2026-10-19 | [Removal notice to “Optimized gated spatiotemporal graph attention network based diagnosis of facial expression through video games” \[Pattern Recognition 175 (2026) 112991\]](https://doi.org/10.1016/j.patcog.2026.114903) | [Pattern Recognition](https://scholar4ai.com/journals/pattern-recognition.md) | Dr. Purushottama Rao K, S Uma, Vijayaraj N et al. |  |
| 2026-10-17 | [TNIA: Target-aware transformer-based node injection attacks on graph neural networks](https://doi.org/10.1016/j.eswa.2026.134772) | [Expert Systems with Applications](https://scholar4ai.com/journals/expert-systems-with-applications.md) | Qiongshan Pan, Peng Bao | Beijing Jiaotong University |
| 2026-10-17 | [Multi-Perspective explainability in traffic prediction: A neuro-symbolic approach using CNN-LSTMs and concept lattices](https://doi.org/10.1007/s10489-026-07512-7) | [Applied Intelligence](https://scholar4ai.com/journals/applied-intelligence.md) | Suraya Syazwani Mohamad Yusof, Hadhrami Ab Ghani, Nurul Izrin Md Saleh et al. | Universiti Malaysia Kelantan; Universiti Teknikal Malaysia Melaka; University of Technology Malaysia |
| 2026-10-17 | [STAGE-Net: Epileptic state-aware graph representation and dynamic modeling for SEEG-based epileptogenic zone localization](https://doi.org/10.1016/j.eswa.2026.134783) | [Expert Systems with Applications](https://scholar4ai.com/journals/expert-systems-with-applications.md) | Zhuoyi Li, Yifan Chen, Ning Zhu et al. | Northwestern Polytechnical University; Xijing Hospital; Air Force Medical University; … |
| 2026-10-17 | [GLCN: a hybrid graph convolution and lite capsule network for robust and interpretable link prediction in complex networks](https://doi.org/10.1007/s10115-026-02906-y) | [Knowledge and Information Systems](https://scholar4ai.com/journals/knowledge-and-information-systems.md) | Indu, Varsha Sisaudia, Kapil Sharma | Delhi Technological University |
| 2026-10-17 | [CasHyper: Modeling multi-factor interactions and asymmetric influence in cascade prediction via hypercomplex algebra](https://doi.org/10.1016/j.ipm.2026.105239) | [Information Processing & Management](https://scholar4ai.com/journals/information-processing-management.md) | Yansong Wang, Qisen Chai, Junjie Huang et al. | Southwest University; Chongqing Normal University |
| 2026-10-17 | [IFCRec: interest-feature dual calibration for graph recommendation](https://doi.org/10.1007/s10489-026-07531-4) | [Applied Intelligence](https://scholar4ai.com/journals/applied-intelligence.md) | Zhenzhen Huang, Weiran Li, Shuo Xiao et al. | China University of Mining and Technology |
| 2026-10-16 | [DGKT: Dual Graph Kernel Transformer for graph classification](https://doi.org/10.1016/j.patcog.2026.115145) | [Pattern Recognition](https://scholar4ai.com/journals/pattern-recognition.md) | Lixiang Xu, Weixin Yu, Zezhou Wang et al. | Hefei University; Hefei Institute of Technology; Beijing Normal University; … |
| 2026-10-16 | [ITEACH-Net: Inverted teacher-student search network for emotion recognition in conversation](https://doi.org/10.1016/j.artint.2026.104643) | [Artificial Intelligence](https://scholar4ai.com/journals/artificial-intelligence.md) | Haiyang Sun, Zheng Lian, Chenglong Wang et al. | Chinese Academy of Sciences; Institute of Automation; University of Chinese Academy of Sciences; … |
| 2026-10-15 | [Learnable eigenfunctions for graph rewiring: Balancing local community structure and global connectivity](https://doi.org/10.1016/j.eswa.2026.134736) | [Expert Systems with Applications](https://scholar4ai.com/journals/expert-systems-with-applications.md) | Waqar Ali, Ahmed Begga, Sebastiano Vascon et al. | Ca' Foscari University of Venice; ZHAW Zurich University of Applied Sciences; University of Alicante; … |
| 2026-10-15 | [A Cognitive, Quantum-Inspired Learning Framework for Energy-Efficient and Reliable Routing in Wireless Body Area Networks](https://doi.org/10.1007/s12559-026-10665-9) | [Cognitive Computation](https://scholar4ai.com/journals/cognitive-computation.md) | Soufiane Ben Othman, Naima Saeed | King Faisal University; University of Aden |
| 2026-10-15 | [Toward class-imbalanced node classification by Causality-Inspired Invariant Representation Disentanglement](https://doi.org/10.1016/j.knosys.2026.117205) | [Knowledge-Based Systems](https://scholar4ai.com/journals/knowledge-based-systems.md) | Xinxin Liu, Jie Cao, Hong Zhao | Minnan Normal University; Hefei University of Technology; Fuzhou University |
| 2026-10-15 | [Adaptive fusion heterogeneous graph attention network for detecting review spammer groups](https://doi.org/10.1016/j.neunet.2026.109735) | [Neural Networks](https://scholar4ai.com/journals/neural-networks.md) | Haoran Peng, Peng Zhang, Ru Ma et al. | Yanshan University; Beijing Institute of Technology |
| 2026-10-15 | [Metropolis-scale resilient and trustworthy traffic flow inference using multi-source data](https://doi.org/10.1016/j.trc.2026.106083) | [Transportation Research Part C Emerging Technologies](https://scholar4ai.com/journals/transportation-research-part-c-emerging-technologies.md) | Qishen Zhou, Yifan Zhang, Michail Makridis et al. | Jilin University; City University of Hong Kong; City University of Hong Kong (Dongguan); … |
| 2026-10-14 | [DiSTA: A distributional semantic graph framework for multi-level information fusion in traffic forecasting](https://doi.org/10.1016/j.inffus.2026.104874) | [Information Fusion](https://scholar4ai.com/journals/information-fusion.md) | Yuanzhang Zhao, Xingfeng Lv, Qianqian Ren | Heilongjiang University |
| 2026-10-14 | [Towards robust Graph Neural Networks: A comprehensive strategy against graph and label noise](https://doi.org/10.1016/j.ipm.2026.105223) | [Information Processing & Management](https://scholar4ai.com/journals/information-processing-management.md) | Jie Chen, Fei Zhu | Soochow University |
| 2026-10-14 | [Distilling representation evolution from GNNs into graph-less MLPs](https://doi.org/10.1016/j.eswa.2026.134729) | [Expert Systems with Applications](https://scholar4ai.com/journals/expert-systems-with-applications.md) | Fuqiang Liu, Jiayan Fu, Xinlong Chen et al. | Fuzhou University |
| 2026-10-14 | [A multi-scale semantic perception network with multi-relational text graphs for text classification](https://doi.org/10.1016/j.eswa.2026.134741) | [Expert Systems with Applications](https://scholar4ai.com/journals/expert-systems-with-applications.md) | Chongxu Hu, Xiaoyan Gongye, Zhe Liu et al. | Qufu Normal University |
| 2026-10-14 | [A biophysically-inspired framework with spatiotemporal graph diffusion for EEG-based mental workload assessment](https://doi.org/10.1016/j.eswa.2026.134730) | [Expert Systems with Applications](https://scholar4ai.com/journals/expert-systems-with-applications.md) | Hui Rong Xiao, Bo Wang, Hengrui Ma et al. | Wuhan University |
| 2026-10-14 | [AAGP: An application-algorithm aware graph partitioning method via cost-sensitive graph neural networks](https://doi.org/10.1016/j.eswa.2026.134709) | [Expert Systems with Applications](https://scholar4ai.com/journals/expert-systems-with-applications.md) | Yuan Liu, Guosun Zeng, Yufei Jin et al. | Tongji University; Xi'an Technological University |
| 2026-10-14 | [Topology-aware dynamic co-evolution for robust graph learning](https://doi.org/10.1016/j.neunet.2026.109736) | [Neural Networks](https://scholar4ai.com/journals/neural-networks.md) | Tingting Zhang, Shuxia Lu, Mengru Wang et al. | Hebei University; Tsinghua University |
| 2026-10-14 | [Domain-adversarial anatomical graph networks for cross-user human activity recognition](https://doi.org/10.1016/j.inffus.2026.104876) | [Information Fusion](https://scholar4ai.com/journals/information-fusion.md) | Xiaozhou Ye, Kevin I‐Kai Wang | University of Auckland |
| 2026-10-13 | [Causal representation regularized heterogeneous graph neural network for robust EEG-fNIRS bimodal emotion recognition](https://doi.org/10.1016/j.eswa.2026.134695) | [Expert Systems with Applications](https://scholar4ai.com/journals/expert-systems-with-applications.md) | Yushun Xiao, Cheng Lu, Tao Zhao et al. | Southeast University |
| 2026-10-12 | [Multi-task end-to-end portfolio optimization with self-supervised graph attention network](https://doi.org/10.1016/j.eswa.2026.134674) | [Expert Systems with Applications](https://scholar4ai.com/journals/expert-systems-with-applications.md) | Yinhong Yao, Yupeng Wang, Jingjing Li et al. | Capital University of Economics and Business |
| 2026-10-10 | [TACoS: Weakly supervised learning of two-dimensional materials from scribble annotations to precise segmentation](https://doi.org/10.1016/j.patcog.2026.115084) | [Pattern Recognition](https://scholar4ai.com/journals/pattern-recognition.md) | Jiabei Chen, Liping Zhang, Jiangbin Wu et al. | Chinese Academy of Sciences; Institute of Semiconductors; University of Chinese Academy of Sciences |
| 2026-10-09 | [Decoupled reverse Kullback–Leibler: Rethinking knowledge distillation loss for bridging GNNs and MLPs](https://doi.org/10.1016/j.patcog.2026.115090) | [Pattern Recognition](https://scholar4ai.com/journals/pattern-recognition.md) | Shaokai Xu, Muyang Li, Qiyan Huang et al. | Qingdao University of Science and Technology; University of Chinese Academy of Sciences; Sino-Danish Centre for Education and Research |
| 2026-10-09 | [Contrastive semi-supervised clustering based on pairwise constraint for identifying influential nodes in complex networks](https://doi.org/10.1016/j.eswa.2026.134684) | [Expert Systems with Applications](https://scholar4ai.com/journals/expert-systems-with-applications.md) | Bing Sun, Yanmei Hu, Jie Wei et al. | Chengdu University of Technology |
| 2026-10-09 | [Learning attention-enhanced relation-sensitive knowledge graph embeddings with variable receptive fields for link prediction](https://doi.org/10.1016/j.ipm.2026.105215) | [Information Processing & Management](https://scholar4ai.com/journals/information-processing-management.md) | Wanxin Zeng, Yuxin Ye, Zhezhe Xing et al. | Jilin University; Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University |
| 2026-10-09 | [Architecture-agnostic knowledge distillation for machine-learning interatomic potentials](https://doi.org/10.1016/j.neunet.2026.109742) | [Neural Networks](https://scholar4ai.com/journals/neural-networks.md) | Chen Wang, Siyu Hu, Guangming Tan et al. | Institute of Computing Technology |
| 2026-10-09 | [Reliability-aware dynamic dependency graph neural network for airborne network intrusion detection](https://doi.org/10.1016/j.patcog.2026.115103) | [Pattern Recognition](https://scholar4ai.com/journals/pattern-recognition.md) | Wenqi Liu, Maohui Zhou, Cong Gao et al. | Nanjing University of Aeronautics and Astronautics |
| 2026-10-09 | [EEG-UDAF: A novel unsupervised domain adaptation framework leveraging dual-view frequency and spatio-temporal features for EEG-based emotion recognition](https://doi.org/10.1186/s40537-026-01584-5) | [Journal Of Big Data](https://scholar4ai.com/journals/journal-of-big-data.md) | Yufei Chen, Gang Zhou, Pengwei Wang et al. | Zhengzhou University |
| 2026-10-08 | [A structure-guided reinforcement learning framework for joint scheduling and acceptance in R&D projects under technical risk](https://doi.org/10.1016/j.cor.2026.107702) | [Computers & Operations Research](https://scholar4ai.com/journals/computers-operations-research.md) | Xinyue Wang, Chaoming Hu, Haojun Fang et al. | Hefei University of Technology |
| 2026-10-08 | [A novel graph-based patient embedding method for the diagnosis of Alzheimer’s disease from microRNA expression data](https://doi.org/10.1007/s10618-026-01275-y) | [Data Mining and Knowledge Discovery](https://scholar4ai.com/journals/data-mining-and-knowledge-discovery.md) | Veronica Buttaro, Antonio Pellicani, Gianvito Pio et al. | University of Bari Aldo Moro; Consorzio Interuniversitario Nazionale per l'Informatica; National Research Council; … |
| 2026-10-08 | [A stability-validated unsupervised anomaly detection framework for identifying suspicious pre-listing trading behavior in cryptocurrency markets](https://doi.org/10.1007/s42521-026-00227-x) | [Digital Finance](https://scholar4ai.com/journals/digital-finance.md) | Gela Tsuladze, Frédérik Sinan Bernard, Marcos Machado | University of Twente |
| 2026-10-08 | [HAPO: Hierarchical affinity aware propagation for unsupervised graph anomaly detection](https://doi.org/10.1016/j.patcog.2026.115062) | [Pattern Recognition](https://scholar4ai.com/journals/pattern-recognition.md) | Huahua Ding, Chaofan Dai, Haohao Zhou et al. | National University of Defense Technology |
| 2026-10-08 | [Beyond topology-driven graph convolution: Node patch convolutional network for node representation learning](https://doi.org/10.1016/j.patcog.2026.115100) | [Pattern Recognition](https://scholar4ai.com/journals/pattern-recognition.md) | Jinsong Chen, TONG Mingwen, Hao Fan et al. | Guangxi Normal University; Central China Normal University; Wuhan University; … |
| 2026-10-07 | [Distributionally-robust heterogeneous graph neural networks via relation-aware grouping](https://doi.org/10.1016/j.ipm.2026.105199) | [Information Processing & Management](https://scholar4ai.com/journals/information-processing-management.md) | Yunfei Wang, Yanghui Fu, Shixuan Liu et al. | National University of Defense Technology; Renmin University of China |
| 2026-10-07 | [Information-aware multi-behavior processing for purchase decision prediction via cascaded graph and hypergraph learning](https://doi.org/10.1016/j.ipm.2026.105221) | [Information Processing & Management](https://scholar4ai.com/journals/information-processing-management.md) | Quan Yang, Bin Yu | Hunan Normal University |
| 2026-10-06 | [Learn from historical subgraph for temporal knowledge graph extrapolation reasoning](https://doi.org/10.1016/j.knosys.2026.117132) | [Knowledge-Based Systems](https://scholar4ai.com/journals/knowledge-based-systems.md) | Lin Zhu, Xin Ren, Luyi Bai | North Minzu University; Eastern University |
| 2026-10-06 | [Anomaly detection in SAP S/4HANA using hybrid deep learning for multivariate time series data](https://doi.org/10.1186/s40537-026-01572-9) | [Journal Of Big Data](https://scholar4ai.com/journals/journal-of-big-data.md) | Ram Reddy Jonnalagadda, B. P. Joshi, Kiran Kumar Reddy et al. | Osmania University; Graphic Era Hill University; Graphic Era University; … |
| 2026-10-06 | [FedGNN: Decentralized federated GNN with gradient masking and dynamic feature pruning for heterogeneous ECG classification](https://doi.org/10.1016/j.eswa.2026.134644) | [Expert Systems with Applications](https://scholar4ai.com/journals/expert-systems-with-applications.md) | N. M. Istiak Chowdhury, Tanvir Mahtab Tapu, Md. Shahriar Shakil et al. |  |

## Cite this page

Scholar4AI. (2026). Graph neural network (graph convolution). Journal Research Rankings. Retrieved October 26, 2026, from https://scholar4ai.com/equations/graph-neural-network-graph-convolution

```bibtex
@misc{scholar4ai-equations-graph-neural-network-graph-convolution,
  author = {{Scholar4AI}},
  title = {Graph neural network (graph convolution)},
  year = {2026},
  howpublished = {\url{https://scholar4ai.com/equations/graph-neural-network-graph-convolution}},
  urldate = {2026-10-26},
  note = {Journal Research Rankings; data from OpenAlex (CC0); licensed CC BY-NC 4.0}
}
```

License: CC BY-NC 4.0 (https://creativecommons.org/licenses/by-nc/4.0/).