A '''graph neural network''' (GNN)''' is a class of [[Neural network|neural networks]] for processing data represented by [[Graph (abstract data type)|graph data structures]]<ref>{{Cite journal|last=Scarselli|first=Franco|last2=Gori|first2=Marco|last3=Tsoi|first3=Ah Chung|last4=Hagenbuchner|first4=Markus|last5=Monfardini|first5=Gabriele|date=2009|title=The Graph Neural Network Model|url=https://ieeexplore.ieee.org/abstract/document/4700287|journal=IEEE Transactions on Neural Networks|volume=20|issue=1|pages=61–80|doi=10.1109/TNN.2008.2005605|issn=1941-0093}}</ref>. They were popularized by their use in [[supervised learning]] on properties of various molecules<ref>{{Cite journal|last=Gilmer|first=Justin|last2=Schoenholz|first2=Samuel S.|last3=Riley|first3=Patrick F.|last4=Vinyals|first4=Oriol|last5=Dahl|first5=George E.|date=2017-07-17|title=Neural Message Passing for Quantum Chemistry|url=http://proceedings.mlr.press/v70/gilmer17a.html|journal=International Conference on Machine Learning|language=en|publisher=PMLR|pages=1263–1272}}</ref>.
Since their inception, several variants of the simple message passing neural network (MPNN) framework have been proposed<ref>{{Cite journal|last=Kipf|first=Thomas N|last2=Welling|first2=Max|date=2016|title=Semi-supervised classification with graph convolutional networks|url=https://ieeexplore.ieee.org/abstract/document/4700287|journal=International Conference on Learning Representations|volume=5|via=arXiv}}</ref><ref>{{Cite journal|last=Defferrard|first=Michaël|last2=Bresson|first2=Xavier|last3=Vandergheynst|first3=Pierre|date=2017-02-05|title=Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering|url=http://arxiv.org/abs/1606.09375|journal=Neural Information Processing Systems|volume=30}}</ref><ref>{{Cite journal|last=Hamilton|first=William|last2=Ying|first2=Rex|last3=Leskovec|first3=Jure|date=2017|title=Inductive Representation Learning on Large Graphs|url=https://cs.stanford.edu/people/jure/pubs/graphsage-nips17.pdf|journal=Neural Information Processing Systems|volume=31|via=Stanford}}</ref><ref>{{Cite journal|last=Veličković|first=Petar|last2=Cucurull|first2=Guillem|last3=Casanova|first3=Arantxa|last4=Romero|first4=Adriana|last5=Liò|first5=Pietro|last6=Bengio|first6=Yoshua|date=2018-02-04|title=Graph Attention Networks|url=http://arxiv.org/abs/1710.10903|journal=International Conference on Learning Representations|volume=6}}</ref>. These models optimize GNNs for use on larger graphs and apply them to domains such as [[Social network|social networks]], [[Citation graph|citation networks]], and online communities<ref>{{Cite web|title=Stanford Large Network Dataset Collection|url=https://snap.stanford.edu/data/|access-date=2021-07-05|website=snap.stanford.edu}}</ref>.
It has been mathematically proven that GNNs are a weak form of the Weisfeiler-LehmanWeisfeiler–Lehman graph isomorphism test<ref>{{Cite journal|last=Douglas|first=B. L.|date=2011-01-27|title=The Weisfeiler-LehmanWeisfeiler–Lehman Method and Graph Isomorphism Testing|url=http://arxiv.org/abs/1101.5211|journal=arXiv:1101.5211 [math]}}</ref>, so any GNN model is at least as powerful as this test<ref>{{Cite journal|last=Xu|first=Keyulu|last2=Hu|first2=Weihua|last3=Leskovec|first3=Jure|last4=Jegelka|first4=Stefanie|date=2019-02-22|title=How Powerful are Graph Neural Networks?|url=http://arxiv.org/abs/1810.00826|journal=International Conference on Learning Representations|volume=7}}</ref>. There is now growing interest in uniting GNNs with other so-called "geometric deep learning models"<ref>{{Cite journal|last=Bronstein|first=Michael M.|last2=Bruna|first2=Joan|last3=LeCun|first3=Yann|last4=Szlam|first4=Arthur|last5=Vandergheynst|first5=Pierre|date=2017|title=Geometric Deep Learning: Going beyond Euclidean data|url=https://ieeexplore.ieee.org/document/7974879/|journal=IEEE Signal Processing Magazine|volume=34|issue=4|pages=18–42|doi=10.1109/MSP.2017.2693418|issn=1053-5888}}</ref> to better understand how and why these models work.
