# Multi-hop Convolutions on Weighted Graphs

arXiv: https://arxiv.org/abs/1911.04978 · HTML: https://mlsanity.com/paper/1911.04978/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Nov 2019.

## Built on by (most cited first, 7 of 7)

- [Multi-modal Graph Learning for Disease Prediction](https://mlsanity.com/paper/2203.05880/) (2022)
- [Towards Accurate and Compact Architectures via Neural Architecture Transformer](https://mlsanity.com/paper/2102.10301/) (2021)
- [From Cluster Assumption to Graph Convolution: Graph-based Semi-Supervised Learning Revisited](https://mlsanity.com/paper/2309.13599/) (2023)
- [Rethinking GNNs and Missing Features: Challenges, Evaluation and a Robust Solution](https://mlsanity.com/paper/2601.04855/) (2026)
- [Relational Graph Neural Network Design via Progressive Neural Architecture Search](https://mlsanity.com/paper/2105.14490/) (2021)
- [Multi-modal Graph Learning for Disease Prediction](https://mlsanity.com/paper/2107.00206/) (2021)
- [When Missingness Follows the Graph: Beyond Feature Propagation for Missing Features](https://mlsanity.com/paper/2610.18113/) (2026)

## Abstract (arXiv)

Graph Convolutional Networks (GCNs) have made significant advances in semi-supervised learning, especially for classification tasks. However, existing GCN based methods have two main drawbacks. First, to increase the receptive field and improve the representation capability of GCNs, larger kernels or deeper network architectures are used, which greatly increases the computational complexity and the number of parameters. Second, methods working on higher order graphs computed directly from adjacency matrices may alter the relationship between graph nodes, particularly for weighted graphs. In addition, the direct construction of higher-order graphs introduces redundant information, which may result in lower network performance. To address the above weaknesses, in this paper, we propose a new method of multi-hop convolutional network on weighted graphs. The proposed method consists of multiple convolutional branches, where each branch extracts node representation from a k-hop graph with small kernels. Such design systematically aggregates multi-scale contextual information without adding redundant information. Furthermore, to efficiently combine the extracted information from the multi-hop branches, an adaptive weight computation (AWC) layer is proposed. We demonstrate the superiority of our MultiHop in six publicly available datasets, including three citation network datasets and three medical image datasets. The experimental results show that our proposed MultiHop method achieves the highest classification accuracy and outperforms the state-of-the-art methods. The source code of this work have been released on GitHub (https://github.com/ahukui/Multi-hop-Convolutions-on-Weighted-Graphs).