This paper investigates the mechanisms and limitations of graph convolutional networks (GCNs) for semi-supervised learning. The authors show that the graph convolution in GCNs is a special form of Laplacian smoothing, which helps in making features of similar vertices more similar, thus improving classification. However, this also leads to potential over-smoothing issues when using many convolutional layers. To address these limitations, the authors propose co-training and self-training approaches to train GCNs. These methods significantly improve GCNs in learning with very few labels and eliminate the need for additional labeled data for validation. Extensive experiments on benchmarks verify the effectiveness of these approaches. GCNs are a type of neural network designed for graph-structured data. They generalize traditional convolutional networks to graphs by using graph convolution operations. The key idea is to apply a graph convolution matrix to the feature matrix, which helps in propagating features across the graph. The authors show that this graph convolution is essentially a form of Laplacian smoothing, which helps in making features of similar vertices more similar. However, repeated applications of this smoothing can lead to over-smoothing, where features of different clusters become indistinguishable. The authors propose co-training and self-training methods to overcome these limitations. Co-training involves training a GCN with a random walk model to explore the global graph structure, while self-training uses the GCN's feature extraction capability to improve its performance. Combining both methods significantly improves the GCN model for semi-supervised learning with very few labels. The paper also discusses the challenges of training deep GCNs, such as the difficulty in training and the risk of over-smoothing. The authors propose solutions to these issues, including the use of co-training and self-training methods. The experiments show that these methods outperform traditional GCNs and other semi-supervised learning methods, especially when labeled data is scarce. The results demonstrate that the proposed methods are effective in improving the performance of GCNs for semi-supervised learning.This paper investigates the mechanisms and limitations of graph convolutional networks (GCNs) for semi-supervised learning. The authors show that the graph convolution in GCNs is a special form of Laplacian smoothing, which helps in making features of similar vertices more similar, thus improving classification. However, this also leads to potential over-smoothing issues when using many convolutional layers. To address these limitations, the authors propose co-training and self-training approaches to train GCNs. These methods significantly improve GCNs in learning with very few labels and eliminate the need for additional labeled data for validation. Extensive experiments on benchmarks verify the effectiveness of these approaches. GCNs are a type of neural network designed for graph-structured data. They generalize traditional convolutional networks to graphs by using graph convolution operations. The key idea is to apply a graph convolution matrix to the feature matrix, which helps in propagating features across the graph. The authors show that this graph convolution is essentially a form of Laplacian smoothing, which helps in making features of similar vertices more similar. However, repeated applications of this smoothing can lead to over-smoothing, where features of different clusters become indistinguishable. The authors propose co-training and self-training methods to overcome these limitations. Co-training involves training a GCN with a random walk model to explore the global graph structure, while self-training uses the GCN's feature extraction capability to improve its performance. Combining both methods significantly improves the GCN model for semi-supervised learning with very few labels. The paper also discusses the challenges of training deep GCNs, such as the difficulty in training and the risk of over-smoothing. The authors propose solutions to these issues, including the use of co-training and self-training methods. The experiments show that these methods outperform traditional GCNs and other semi-supervised learning methods, especially when labeled data is scarce. The results demonstrate that the proposed methods are effective in improving the performance of GCNs for semi-supervised learning.