# Higher-order Graph Convolutional Networks

arXiv: https://arxiv.org/abs/1809.07697 · HTML: https://mlsanity.com/paper/1809.07697/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Sep 2018.

## Built on by (most cited first, 8 of 8)

- [Size-Invariant Graph Representations for Graph Classification Extrapolations](https://mlsanity.com/paper/2103.05045/) (2021)
- [Hamba: Single-view 3D Hand Reconstruction with Graph-guided Bi-Scanning Mamba](https://mlsanity.com/paper/2407.09646/) (2024)
- [Higher-order Clustering and Pooling for Graph Neural Networks](https://mlsanity.com/paper/2209.03473/) (2022)
- [A Hypergraph Neural Network Framework for Learning Hyperedge-Dependent Node Embeddings](https://mlsanity.com/paper/2212.14077/) (2022)
- [GCN-ALP: Addressing Matching Collisions in Anchor Link Prediction](https://mlsanity.com/paper/2103.10600/) (2021)
- [Relational Graph Neural Network Design via Progressive Neural Architecture Search](https://mlsanity.com/paper/2105.14490/) (2021)
- [Studying and Improving Graph Neural Network-based Motif Estimation](https://mlsanity.com/paper/2506.15709/) (2025)
- [Node Classification via Simplicial Interaction with Augmented Maximal Clique Selection](https://mlsanity.com/paper/2509.23568/) (2025)

## Abstract (arXiv)

Following the success of deep convolutional networks in various vision and speech related tasks, researchers have started investigating generalizations of the well-known technique for graph-structured data. A recently-proposed method called Graph Convolutional Networks has been able to achieve state-of-the-art results in the task of node classification. However, since the proposed method relies on localized first-order approximations of spectral graph convolutions, it is unable to capture higher-order interactions between nodes in the graph. In this work, we propose a motif-based graph attention model, called Motif Convolutional Networks (MCNs), which generalizes past approaches by using weighted multi-hop motif adjacency matrices to capture higher-order neighborhoods. A novel attention mechanism is used to allow each individual node to select the most relevant neighborhood to apply its filter. Experiments show that our proposed method is able to achieve state-of-the-art results on the semi-supervised node classification task.