The Graph Neural Network Model

Franco Scarselli; M. Gori; Ah Chung Tsoi; Markus Hagenbuchner; Gabriele Monfardini

doi:https://doi.org/10.1109/tnn.2008.2005605

The Graph Neural Network Model

2008 · IEEE Transactions on Neural Networks · 9,662 citations · 18 from inside this corpus

Franco Scarselli, M. Gori low, Ah Chung Tsoi, Markus Hagenbuchner, Gabriele Monfardini

Many underlying relationships among data in several areas of science and engineering, e.g., computer vision, molecular chemistry, molecular biology, pattern recognition, and data mining, can be represented in terms of graphs. In this paper, we propose a new neural network model, called graph neural network (GNN) model, that extends existing neural network methods for processing the data represented in graph domains. This GNN model, which can directly process most of the practically useful types of graphs, e.g., acyclic, cyclic, directed, and undirected, implements a function tau(G,n) is an element of IR(m) that maps a graph G and one of its nodes n into an m-dimensional Euclidean space. A supervised learning algorithm is derived to estimate the parameters of the proposed GNN model. The computational cost of the proposed algorithm is also considered. Some experimental results are shown to validate the proposed learning algorithm, and to demonstrate its generalization capabilities.

36 of 36 neighbouring works in this corpus. Blue is what this paper cites; orange is what cites it, and a dashed line is one neighbour citing another. Only the largest labels are drawn — every node carries its full title on hover.

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Citation edge evidence

Each row is directed from the citing work to the cited work. Source status remains readable without the interactive graph.

A Comprehensive Survey on Graph Neural Networks→The Graph Neural Network ModelLegacy edge — source detail unavailable
Semi-Supervised Classification with Graph Convolutional Networks→The Graph Neural Network ModelLegacy edge — source detail unavailable
Graph neural networks: A review of methods and applications→The Graph Neural Network ModelLegacy edge — source detail unavailable
Modeling Relational Data with Graph Convolutional Networks→The Graph Neural Network ModelLegacy edge — source detail unavailable
Convolutional Neural Networks On Graphs With Fast Localized Spectral Filtering (Netsci-X'…→The Graph Neural Network ModelLegacy edge — source detail unavailable
A Comprehensive Survey on Graph Neural Networks→The Graph Neural Network ModelLegacy edge — source detail unavailable
Heterogeneous Graph Attention Network→The Graph Neural Network ModelLegacy edge — source detail unavailable
Graph Convolutional Neural Networks for Web-Scale Recommender Systems→The Graph Neural Network ModelLegacy edge — source detail unavailable
Relational inductive biases, deep learning, and graph networks→The Graph Neural Network ModelLegacy edge — source detail unavailable
On the Opportunities and Risks of Foundation Models→The Graph Neural Network ModelLegacy edge — source detail unavailable
A Comprehensive Survey of Graph Embedding: Problems, Techniques, and Applications→The Graph Neural Network ModelLegacy edge — source detail unavailable
Graph convolutional networks: a comprehensive review→The Graph Neural Network ModelLegacy edge — source detail unavailable
Knowledge Graphs→The Graph Neural Network ModelLegacy edge — source detail unavailable
Hypergraph Neural Networks→The Graph Neural Network ModelLegacy edge — source detail unavailable
Deep Learning on Graphs: A Survey→The Graph Neural Network ModelLegacy edge — source detail unavailable
An End-to-End Deep Learning Architecture for Graph Classification→The Graph Neural Network ModelLegacy edge — source detail unavailable
Graph Neural Networks: A Review of Methods and Applications→The Graph Neural Network ModelLegacy edge — source detail unavailable
Explaining Deep Neural Networks and Beyond: A Review of Methods and Applications→The Graph Neural Network ModelLegacy edge — source detail unavailable
The Graph Neural Network Model→Neural Networks: A Comprehensive FoundationLegacy edge — source detail unavailable
The Graph Neural Network Model→Statistical Learning TheoryLegacy edge — source detail unavailable
The Graph Neural Network Model→Neural networks for pattern recognitionLegacy edge — source detail unavailable
The Graph Neural Network Model→Parallel Distributed ProcessingLegacy edge — source detail unavailable
The Graph Neural Network Model→Conditional Random Fields: Probabilistic Models for Segmenting and Labeling Sequence DataLegacy edge — source detail unavailable
The Graph Neural Network Model→Neural Networks for Pattern RecognitionLegacy edge — source detail unavailable
The Graph Neural Network Model→Advances in Neural Information Processing Systems 14Legacy edge — source detail unavailable
The Graph Neural Network Model→Lecture Notes in Artificial IntelligenceLegacy edge — source detail unavailable
The Graph Neural Network Model→Neural networks: A comprehensive foundationLegacy edge — source detail unavailable
The Graph Neural Network Model→Semi-Supervised LearningLegacy edge — source detail unavailable
The Graph Neural Network Model→A direct adaptive method for faster backpropagation learning: the RPROP algorithmLegacy edge — source detail unavailable
The Graph Neural Network Model→Advances in Neural Information Processing Systems 37Legacy edge — source detail unavailable
The Graph Neural Network Model→Universal Approximation using Incremental Constructive Feedforward Networks with Random H…Legacy edge — source detail unavailable
The Graph Neural Network Model→Introduction to Bayesian NetworksLegacy edge — source detail unavailable
The Graph Neural Network Model→The Cascade-Correlation learning architectureLegacy edge — source detail unavailable
The Graph Neural Network Model→A new model for learning in graph domainsLegacy edge — source detail unavailable
The Graph Neural Network Model→Pruning algorithms-a surveyLegacy edge — source detail unavailable
The Graph Neural Network Model→Introduction to Statistical Relational LearningLegacy edge — source detail unavailable
Semi-Supervised Learning→Statistical Learning TheoryLegacy edge — source detail unavailable
Semi-Supervised Learning→Neural Networks for Pattern RecognitionLegacy edge — source detail unavailable
Universal Approximation using Incremental Constructive Feedforward Networks with Random H…→Statistical Learning TheoryLegacy edge — source detail unavailable
A direct adaptive method for faster backpropagation learning: the RPROP algorithm→Parallel Distributed ProcessingLegacy edge — source detail unavailable
Semi-Supervised Classification with Graph Convolutional Networks→A new model for learning in graph domainsLegacy edge — source detail unavailable
Semi-Supervised Classification with Graph Convolutional Networks→Convolutional Neural Networks On Graphs With Fast Localized Spectral Filtering (Netsci-X'…Legacy edge — source detail unavailable
Modeling Relational Data with Graph Convolutional Networks→Semi-Supervised Classification with Graph Convolutional NetworksLegacy edge — source detail unavailable
An End-to-End Deep Learning Architecture for Graph Classification→Convolutional Neural Networks On Graphs With Fast Localized Spectral Filtering (Netsci-X'…Legacy edge — source detail unavailable
Relational inductive biases, deep learning, and graph networks→A new model for learning in graph domainsLegacy edge — source detail unavailable
Relational inductive biases, deep learning, and graph networks→Introduction to Statistical Relational LearningLegacy edge — source detail unavailable
Hypergraph Neural Networks→A new model for learning in graph domainsLegacy edge — source detail unavailable
Hypergraph Neural Networks→Semi-Supervised Classification with Graph Convolutional NetworksLegacy edge — source detail unavailable
Graph Neural Networks: A Review of Methods and Applications→A new model for learning in graph domainsLegacy edge — source detail unavailable
Graph Neural Networks: A Review of Methods and Applications→Modeling Relational Data with Graph Convolutional NetworksLegacy edge — source detail unavailable
Graph Neural Networks: A Review of Methods and Applications→An End-to-End Deep Learning Architecture for Graph ClassificationLegacy edge — source detail unavailable
Graph Neural Networks: A Review of Methods and Applications→Relational inductive biases, deep learning, and graph networksLegacy edge — source detail unavailable
Graph Neural Networks: A Review of Methods and Applications→Hypergraph Neural NetworksLegacy edge — source detail unavailable
Graph Neural Networks: A Review of Methods and Applications→Heterogeneous Graph Attention NetworkLegacy edge — source detail unavailable
Graph Neural Networks: A Review of Methods and Applications→A Comprehensive Survey of Graph Embedding: Problems, Techniques, and ApplicationsLegacy edge — source detail unavailable
Graph Neural Networks: A Review of Methods and Applications→Convolutional Neural Networks On Graphs With Fast Localized Spectral Filtering (Netsci-X'…Legacy edge — source detail unavailable
Graph Neural Networks: A Review of Methods and Applications→Graph convolutional networks: a comprehensive reviewLegacy edge — source detail unavailable
Graph Neural Networks: A Review of Methods and Applications→Deep Learning on Graphs: A SurveyLegacy edge — source detail unavailable
Graph Neural Networks: A Review of Methods and Applications→A Comprehensive Survey on Graph Neural NetworksLegacy edge — source detail unavailable
A Comprehensive Survey on Graph Neural Networks→A new model for learning in graph domainsLegacy edge — source detail unavailable
A Comprehensive Survey on Graph Neural Networks→Graph Convolutional Neural Networks for Web-Scale Recommender SystemsLegacy edge — source detail unavailable
A Comprehensive Survey on Graph Neural Networks→Heterogeneous Graph Attention NetworkLegacy edge — source detail unavailable
A Comprehensive Survey on Graph Neural Networks→A Comprehensive Survey of Graph Embedding: Problems, Techniques, and ApplicationsLegacy edge — source detail unavailable
Heterogeneous Graph Attention Network→A new model for learning in graph domainsLegacy edge — source detail unavailable
Heterogeneous Graph Attention Network→Semi-Supervised Classification with Graph Convolutional NetworksLegacy edge — source detail unavailable
Heterogeneous Graph Attention Network→Modeling Relational Data with Graph Convolutional NetworksLegacy edge — source detail unavailable
Heterogeneous Graph Attention Network→Convolutional Neural Networks On Graphs With Fast Localized Spectral Filtering (Netsci-X'…Legacy edge — source detail unavailable
A Comprehensive Survey of Graph Embedding: Problems, Techniques, and Applications→Convolutional Neural Networks On Graphs With Fast Localized Spectral Filtering (Netsci-X'…Legacy edge — source detail unavailable
Graph convolutional networks: a comprehensive review→Semi-Supervised Classification with Graph Convolutional NetworksLegacy edge — source detail unavailable
Graph convolutional networks: a comprehensive review→Graph Convolutional Neural Networks for Web-Scale Recommender SystemsLegacy edge — source detail unavailable
Graph convolutional networks: a comprehensive review→Graph Neural Networks: A Review of Methods and ApplicationsLegacy edge — source detail unavailable
Graph convolutional networks: a comprehensive review→A Comprehensive Survey on Graph Neural NetworksLegacy edge — source detail unavailable
Graph convolutional networks: a comprehensive review→A Comprehensive Survey of Graph Embedding: Problems, Techniques, and ApplicationsLegacy edge — source detail unavailable
Graph convolutional networks: a comprehensive review→A Comprehensive Survey on Graph Neural NetworksLegacy edge — source detail unavailable
Knowledge Graphs→Introduction to Statistical Relational LearningLegacy edge — source detail unavailable
Knowledge Graphs→Heterogeneous Graph Attention NetworkLegacy edge — source detail unavailable
Knowledge Graphs→A Comprehensive Survey on Graph Neural NetworksLegacy edge — source detail unavailable
Deep Learning on Graphs: A Survey→A new model for learning in graph domainsLegacy edge — source detail unavailable
Deep Learning on Graphs: A Survey→Modeling Relational Data with Graph Convolutional NetworksLegacy edge — source detail unavailable
Deep Learning on Graphs: A Survey→An End-to-End Deep Learning Architecture for Graph ClassificationLegacy edge — source detail unavailable
Deep Learning on Graphs: A Survey→Relational inductive biases, deep learning, and graph networksLegacy edge — source detail unavailable
Deep Learning on Graphs: A Survey→Graph Convolutional Neural Networks for Web-Scale Recommender SystemsLegacy edge — source detail unavailable
Deep Learning on Graphs: A Survey→A Comprehensive Survey on Graph Neural NetworksLegacy edge — source detail unavailable
Deep Learning on Graphs: A Survey→Heterogeneous Graph Attention NetworkLegacy edge — source detail unavailable
Deep Learning on Graphs: A Survey→Graph convolutional networks: a comprehensive reviewLegacy edge — source detail unavailable
Deep Learning on Graphs: A Survey→Graph neural networks: A review of methods and applicationsLegacy edge — source detail unavailable
Explaining Deep Neural Networks and Beyond: A Review of Methods and Applications→Neural networks for pattern recognitionLegacy edge — source detail unavailable
Explaining Deep Neural Networks and Beyond: A Review of Methods and Applications→Neural Networks for Pattern RecognitionLegacy edge — source detail unavailable
Graph neural networks: A review of methods and applications→A new model for learning in graph domainsLegacy edge — source detail unavailable
Graph neural networks: A review of methods and applications→Modeling Relational Data with Graph Convolutional NetworksLegacy edge — source detail unavailable
Graph neural networks: A review of methods and applications→An End-to-End Deep Learning Architecture for Graph ClassificationLegacy edge — source detail unavailable
Graph neural networks: A review of methods and applications→Relational inductive biases, deep learning, and graph networksLegacy edge — source detail unavailable
Graph neural networks: A review of methods and applications→Hypergraph Neural NetworksLegacy edge — source detail unavailable
Graph neural networks: A review of methods and applications→Heterogeneous Graph Attention NetworkLegacy edge — source detail unavailable
Graph neural networks: A review of methods and applications→A Comprehensive Survey of Graph Embedding: Problems, Techniques, and ApplicationsLegacy edge — source detail unavailable
Graph neural networks: A review of methods and applications→Graph convolutional networks: a comprehensive reviewLegacy edge — source detail unavailable
Graph neural networks: A review of methods and applications→A Comprehensive Survey on Graph Neural NetworksLegacy edge — source detail unavailable
A Comprehensive Survey on Graph Neural Networks→A new model for learning in graph domainsLegacy edge — source detail unavailable
A Comprehensive Survey on Graph Neural Networks→Modeling Relational Data with Graph Convolutional NetworksLegacy edge — source detail unavailable
A Comprehensive Survey on Graph Neural Networks→An End-to-End Deep Learning Architecture for Graph ClassificationLegacy edge — source detail unavailable
A Comprehensive Survey on Graph Neural Networks→Relational inductive biases, deep learning, and graph networksLegacy edge — source detail unavailable
A Comprehensive Survey on Graph Neural Networks→Heterogeneous Graph Attention NetworkLegacy edge — source detail unavailable
A Comprehensive Survey on Graph Neural Networks→A Comprehensive Survey of Graph Embedding: Problems, Techniques, and ApplicationsLegacy edge — source detail unavailable
A Comprehensive Survey on Graph Neural Networks→Convolutional Neural Networks On Graphs With Fast Localized Spectral Filtering (Netsci-X'…Legacy edge — source detail unavailable

What this paper cites, inside the corpus

Paper	Year	Cited
Neural Networks: A Comprehensive Foundation	1998	29,840
Statistical Learning Theory	1999	26,957
Neural networks for pattern recognition	1994	18,720
Parallel Distributed Processing	1986	15,411
Conditional Random Fields: Probabilistic Models for Segmenting and Labeling Sequence Data	2001	12,994
Neural Networks for Pattern Recognition	1995	12,273
Advances in Neural Information Processing Systems 14	2002	8,961
Lecture Notes in Artificial Intelligence	1999	7,440
Neural networks: A comprehensive foundation	1995	7,270
Semi-Supervised Learning	2006	4,334
A direct adaptive method for faster backpropagation learning: the RPROP algorithm	2002	3,936
Advances in Neural Information Processing Systems 37	2024	2,802
Universal Approximation using Incremental Constructive Feedforward Networks with Random H…	2006	2,636
Introduction to Bayesian Networks	2019	2,594
The Cascade-Correlation learning architecture	2018	2,401
A new model for learning in graph domains	2006	1,944
Pruning algorithms-a survey	1993	1,717
Introduction to Statistical Relational Learning	2007	1,645

What cites it, inside the corpus

Paper	Year	Cited
A Comprehensive Survey on Graph Neural Networks	2020	9,855
Semi-Supervised Classification with Graph Convolutional Networks	2016	8,058
Graph neural networks: A review of methods and applications	2020	5,808
Modeling Relational Data with Graph Convolutional Networks	2018	5,233
Convolutional Neural Networks On Graphs With Fast Localized Spectral Filtering (Netsci-X'…	2016	5,118
A Comprehensive Survey on Graph Neural Networks	2020	3,307
Heterogeneous Graph Attention Network	2019	2,999
Graph Convolutional Neural Networks for Web-Scale Recommender Systems	2018	2,836
Relational inductive biases, deep learning, and graph networks	2018	2,406
On the Opportunities and Risks of Foundation Models	2021	2,265
A Comprehensive Survey of Graph Embedding: Problems, Techniques, and Applications	2018	2,076
Graph convolutional networks: a comprehensive review	2019	1,877
Knowledge Graphs	2021	1,767
Hypergraph Neural Networks	2019	1,720
Deep Learning on Graphs: A Survey	2020	1,560
An End-to-End Deep Learning Architecture for Graph Classification	2018	1,519
Graph Neural Networks: A Review of Methods and Applications	2018	1,448
Explaining Deep Neural Networks and Beyond: A Review of Methods and Applications	2021	1,424

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Topics

Neural Networks and Applications	Computer Science
Graph Theory and Algorithms	Computer Science
Advanced Graph Neural Networks	Computer Science

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