# How Powerful are Graph Neural Networks?

@article{Xu2019HowPA, title={How Powerful are Graph Neural Networks?}, author={Keyulu Xu and Weihua Hu and Jure Leskovec and Stefanie Jegelka}, journal={ArXiv}, year={2019}, volume={abs/1810.00826} }

## 1,992 Citations

A Hierarchy of Graph Neural Networks Based on Learnable Local Features

- Computer Science, MathematicsArXiv
- 2019

This work proposes a hierarchy of GNNs based on their aggregation regions, and derives theoretical results about the discriminative power and feature representation capabilities of each class, and shows how this framework can be utilized to systematically construct arbitrarily powerful GNN's.

THE SURPRISING POWER OF GRAPH NEURAL NET-

- 2020

Graph neural networks (GNNs) are effective models for representation learning on graph-structured data. However, standard GNNs are limited in their expressive power, as they cannot distinguish graphs…

k-hop Graph Neural Networks

- Computer Science, MathematicsNeural Networks
- 2020

K-hop GNNs is proposed, which updates a node's representation by aggregating information not only from its direct neighbors, but from its k-hop neighborhood, and it is shown that the proposed architecture can identify fundamental graph properties.

Graphs, Convolutions, and Neural Networks: From Graph Filters to Graph Neural Networks

- Computer Science, EngineeringIEEE Signal Processing Magazine
- 2020

The role of graph convolutional filters in GNNs is discussed and it is shown that any architecture built with such filters has the fundamental properties of permutation equivariance and stability to changes in the topology.

TOWARDS POWERFUL GRAPH NEURAL NETWORKS: DIVERSITY MATTERS

- 2020

Graph neural networks (GNNs) offer us an effective framework for graph representation learning via layer-wise neighborhood aggregation. Their success is attributed to their expressive power at…

A graph similarity for deep learning

- Computer ScienceNeurIPS
- 2020

A simple and fast GNN model based on transform-sum-cat, which obtains, in comparison with widely used GNN models, a higher accuracy in node classification, a lower absolute error in graph regression, and greater stability in adversarial training of graph generation.

Are Powerful Graph Neural Nets Necessary? A Dissection on Graph Classification

- Computer Science, MathematicsArXiv
- 2019

This work proposes Graph Feature Network (GFN), a simple lightweight neural net defined on a set of graph augmented features, and proves that GFN can be derived by linearizing graph filtering part of GNNs, and leverages it to test the importance of the two parts separately.

Self-supervised Hierarchical Graph Neural Network for Graph Representation

- Computer Science2020 IEEE International Conference on Big Data (Big Data)
- 2020

This work proposes an unsupervised hierarchical neural network, referred as GraPHmax, for obtaining graph level representation and proposes the concept of periphery representation and shows its effectiveness to obtain discriminative features of an input graph.

GNNExplainer: Generating Explanations for Graph Neural Networks

- Computer Science, MathematicsNeurIPS
- 2019

GnExplainer is proposed, the first general, model-agnostic approach for providing interpretable explanations for predictions of any GNN-based model on any graph-based machine learning task.

Towards Expressive Graph Representation

- Computer Science, MathematicsArXiv
- 2020

This work proposes expressive GNN that aggregates the neighborhood of each node with a continuous injective set function, so that a GNN layer maps similar nodes with similar neighborhoods to similarembeddings, different nodes to different embeddings and the equivalent nodes or isomorphic graphs to the same embedDings.

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