This paper provides deeper insights into the Graph Convolutional Network (GCN) model and addresses its fundamental limitations in semi-supervised learning. The authors show that the graph convolution in GCNs is a special form of Laplacian smoothing, which helps mix features of vertices and their neighbors, making the classification task easier. However, this smoothing can lead to over-smoothing with many convolutional layers, causing vertices from different clusters to become indistinguishable. To overcome these limitations, the paper proposes co-training and self-training approaches to train GCNs. Co-training involves using a random walk model to find the most confident vertices and add them to the label set, while self-training uses the most confident predictions from the GCN itself. These methods significantly improve GCNs' performance with very few labeled data and eliminate the need for additional labeled data for validation. Extensive experiments on benchmarks verify the effectiveness of the proposed methods. The key contributions include providing new insights into the GCN model and proposing solutions to enhance its performance in semi-supervised learning.This paper provides deeper insights into the Graph Convolutional Network (GCN) model and addresses its fundamental limitations in semi-supervised learning. The authors show that the graph convolution in GCNs is a special form of Laplacian smoothing, which helps mix features of vertices and their neighbors, making the classification task easier. However, this smoothing can lead to over-smoothing with many convolutional layers, causing vertices from different clusters to become indistinguishable. To overcome these limitations, the paper proposes co-training and self-training approaches to train GCNs. Co-training involves using a random walk model to find the most confident vertices and add them to the label set, while self-training uses the most confident predictions from the GCN itself. These methods significantly improve GCNs' performance with very few labeled data and eliminate the need for additional labeled data for validation. Extensive experiments on benchmarks verify the effectiveness of the proposed methods. The key contributions include providing new insights into the GCN model and proposing solutions to enhance its performance in semi-supervised learning.