Computational Capabilities of Graph Neural Networks
Abstract
In this paper, we will consider the approximation properties of a recently introduced neural network model called graph neural network (GNN), which can be used to process-structured data inputs, e.g., acyclic graphs, cyclic graphs, and directed or undirected graphs. This class of neural networks implements a function tau(G,n) is an element of IR(m) that maps a graph G and one of its nodes n onto an m-dimensional Euclidean space. We characterize the functions that can be approximated by GNNs, in probability, up to any prescribed degree of precision. This set contains the maps that satisfy a property called preservation of the unfolding equivalence, and includes most of the practically useful functions on graphs; the only known exception is when the input graph contains particular patterns of symmetries when unfolding equivalence may not be preserved. The result can be considered an extension of the universal approximation property established for the classic feedforward neural networks (FNNs). Some experimental examples are used to show the computational capabilities of the proposed model.
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A ConceptLink graph for text structure mining
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Graph Neural Networks and Boolean SatisfiabilityPreprint
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Protein–Protein Interfaces: A Graph Neural Network Approach
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Link-based web spam detection using weight properties
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Drug Side Effect Prediction with Deep Learning Molecular Embedding in a Graph-of-Graphs Domain
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Graph Neural Network Based Transient Stability Assessment Considering Topology Changes
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Self-citationKernel Robust Soft Learning Vector Quantization
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Graph Learning Network: A Structure Learning AlgorithmPreprint
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The Probabilistic Liveness Decision Method of Unbounded Petri Nets Based on Machine Learning
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- Authors
- Scarselli, F., Gori, M., Tsoi, A. C., Hagenbuchner, M., & Monfardini, G.
- Affiliations
- University of Siena (IT)
- Hong Kong Baptist University (HK)
- University of Wollongong (AU)
- Venue
- IEEE Transactions on Neural Networks
- Published
- 2009-01
- Volume
- 20
- Issue
- 1
- Pages
- 81-102
- ISSN
- 1045-9227 (ISSN-L)
- 1941-0093
- OpenAlex
- W2150120952
- Cited by
- 225
- References
- 42
- Citations by year
- 2026: 8 · 2025: 16 · 2024: 25 · 2023: 20 · 2022: 32 · 2021: 34 · 2020: 25 · 2019: 17 · 2018: 8 · 2017: 2 · 2016: 1 · 2015: 3 · 2014: 7 · 2013: 8 · 2012: 4
- FWCI
- 7.93
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- IEEE Transactions on Neural Networks (publishedVersion)
- PubMed (publishedVersion)
- HKBU Institutional Repository (Hong Kong Baptist University) (submittedVersion)
- Research Online (University of Wollongong) (submittedVersion)
- Figshare (submittedVersion)
- Use Siena air (University of Siena) (submittedVersion)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Advanced Graph Neural Networks
- Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Graph Theory and Algorithms
- Keywords
- graph neural networks, universal approximation, approximation properties, graph symmetry, structured data, acyclic graphs, cyclic graphs, directed and undirected graphs
- MeSH terms
- Algorithms, Pattern Recognition, Automated, Neural Networks, Computer
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
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