# N-GCN: Multi-scale Graph Convolution for Semi-supervised Node Classification

arXiv: https://arxiv.org/abs/1802.08888 · HTML: https://mlsanity.com/paper/1802.08888/

## Key facts

- Cited by 54 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Feb 2018.

## Built on by (most cited first, 30 of 54)

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- [Affinity Attention Graph Neural Network for Weakly Supervised Semantic Segmentation](https://mlsanity.com/paper/2106.04054/) (2021)
- [Shortest Path Networks for Graph Property Prediction](https://mlsanity.com/paper/2206.01003/) (2022)
- [p-Laplacian Based Graph Neural Networks](https://mlsanity.com/paper/2111.07337/) (2021)
- [SPAGAN: Shortest Path Graph Attention Network](https://mlsanity.com/paper/2101.03464/) (2021)
- [Topological Relational Learning on Graphs](https://mlsanity.com/paper/2110.15529/) (2021)
- [MGNNI: Multiscale Graph Neural Networks with Implicit Layers](https://mlsanity.com/paper/2210.08353/) (2022)
- [Graph2text or Graph2token: A Perspective of Large Language Models for Graph Learning](https://mlsanity.com/paper/2501.01124/) (2025)
- [The Snowflake Hypothesis: Training Deep GNN with One Node One Receptive field](https://mlsanity.com/paper/2308.10051/) (2023)
- [The Effectiveness of Curvature-Based Rewiring and the Role of Hyperparameters in GNNs Revisited](https://mlsanity.com/paper/2407.09381/) (2024)
- [Boosting-GNN: Boosting Algorithm for Graph Networks on Imbalanced Node Classification](https://mlsanity.com/paper/2105.11625/) (2021)
- [SkipNode: On Alleviating Performance Degradation for Deep Graph Convolutional Networks](https://mlsanity.com/paper/2112.11628/) (2021)
- [Towards Digital Twin Oriented Modelling of Complex Networked Systems and Their Dynamics: A Comprehensive Survey](https://mlsanity.com/paper/2202.09363/) (2022)
- [DRIN: Dynamic Relation Interactive Network for Multimodal Entity Linking](https://mlsanity.com/paper/2310.05589/) (2023)
- [Redesigning graph filter-based GNNs to relax the homophily assumption](https://mlsanity.com/paper/2409.08676/) (2024)
- [A Piece-wise Polynomial Filtering Approach for Graph Neural Networks](https://mlsanity.com/paper/2112.03499/) (2021)
- [Simplifying Subgraph Representation Learning for Scalable Link Prediction](https://mlsanity.com/paper/2301.12562/) (2023)
- [From Cluster Assumption to Graph Convolution: Graph-based Semi-Supervised Learning Revisited](https://mlsanity.com/paper/2309.13599/) (2023)
- [The Heterophilic Snowflake Hypothesis: Training and Empowering GNNs for Heterophilic Graphs](https://mlsanity.com/paper/2406.12539/) (2024)
- [Multiscale Laplacian Learning](https://mlsanity.com/paper/2109.03718/) (2021)
- [Haar Wavelet Feature Compression for Quantized Graph Convolutional Networks](https://mlsanity.com/paper/2110.04824/) (2021)
- [A Survey on Service Route and Time Prediction in Instant Delivery: Taxonomy, Progress, and Prospects](https://mlsanity.com/paper/2309.01194/) (2023)
- [Digital Twin-Oriented Complex Networked Systems based on Heterogeneous Node Features and Interaction Rules](https://mlsanity.com/paper/2308.11034/) (2023)
- [EMP: Effective Multidimensional Persistence for Graph Representation Learning](https://mlsanity.com/paper/2401.13713/) (2024)
- [SMASH: Sparse Matrix Atomic Scratchpad Hashing](https://mlsanity.com/paper/2105.14156/) (2021)
- [A Top-down Supervised Learning Approach to Hierarchical Multi-label Classification in Networks](https://mlsanity.com/paper/2203.12569/) (2022)
- [Simplified PCNet with Robustness](https://mlsanity.com/paper/2403.03676/) (2024)

## Abstract (arXiv)

Graph Convolutional Networks (GCNs) have shown significant improvements in semi-supervised learning on graph-structured data. Concurrently, unsupervised learning of graph embeddings has benefited from the information contained in random walks. In this paper, we propose a model: Network of GCNs (N-GCN), which marries these two lines of work. At its core, N-GCN trains multiple instances of GCNs over node pairs discovered at different distances in random walks, and learns a combination of the instance outputs which optimizes the classification objective. Our experiments show that our proposed N-GCN model improves state-of-the-art baselines on all of the challenging node classification tasks we consider: Cora, Citeseer, Pubmed, and PPI. In addition, our proposed method has other desirable properties, including generalization to recently proposed semi-supervised learning methods such as GraphSAGE, allowing us to propose N-SAGE, and resilience to adversarial input perturbations.