# Higher-order Weighted Graph Convolutional Networks

arXiv: https://arxiv.org/abs/1911.04129 · HTML: https://mlsanity.com/paper/1911.04129/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Nov 2019.

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

- [HOT: Higher-Order Dynamic Graph Representation Learning with Efficient Transformers](https://mlsanity.com/paper/2311.18526/) (2023)
- [MOOMIN: Deep Molecular Omics Network for Anti-Cancer Drug Combination Therapy](https://mlsanity.com/paper/2110.15087/) (2021)
- [Demystifying Higher-Order Graph Neural Networks](https://mlsanity.com/paper/2406.12841/) (2024)
- [Relational Graph Neural Network Design via Progressive Neural Architecture Search](https://mlsanity.com/paper/2105.14490/) (2021)
- [GAIM: Attacking Graph Neural Networks via Adversarial Influence Maximization](https://mlsanity.com/paper/2408.10948/) (2024)
- [Scalable Parameter Design for Superconducting Quantum Circuits with Graph Neural Networks](https://mlsanity.com/paper/2411.16354/) (2024)
- [NeuroTree: Hierarchical Functional Brain Pathway Decoding for Mental Health Disorders](https://mlsanity.com/paper/2502.18786/) (2025)
- [STDHL: Spatio-Temporal Dynamic Hypergraph Learning for Wind Power Forecasting](https://mlsanity.com/paper/2412.11393/) (2024)

## Abstract (arXiv)

Graph Convolution Network (GCN) has been recognized as one of the most effective graph models for semi-supervised learning, but it extracts merely the first-order or few-order neighborhood information through information propagation, which suffers performance drop-off for deeper structure. Existing approaches that deal with the higher-order neighbors tend to take advantage of adjacency matrix power. In this paper, we assume a seemly trivial condition that the higher-order neighborhood information may be similar to that of the first-order neighbors. Accordingly, we present an unsupervised approach to describe such similarities and learn the weight matrices of higher-order neighbors automatically through Lasso that minimizes the feature loss between the first-order and higher-order neighbors, based on which we formulate the new convolutional filter for GCN to learn the better node representations. Our model, called higher-order weighted GCN(HWGCN), has achieved the state-of-the-art results on a number of node classification tasks over Cora, Citeseer and Pubmed datasets.