Graph Convolutional Networks (GCNs) are powerful deep learning models for graph-structured data, but they often suffer from over-smoothing, leading to shallow models that struggle to extract high-order information. This paper addresses the over-smoothing problem by proposing GCNII, an extension of the vanilla GCN model with two techniques: Initial Residual and Identity Mapping. These techniques effectively alleviate over-smoothing and enable the model to achieve state-of-the-art performance on various semi-supervised and full-supervised tasks. Theoretical and empirical evidence supports the effectiveness of these techniques, demonstrating that GCNII can express polynomial filters with arbitrary coefficients, thus preventing over-smoothing even in deep networks. Experiments on multiple datasets show that GCNII outperforms existing methods, including deep models like JKNet and DropEdge. The paper also provides a spectral analysis of GCNII, showing that it can express arbitrary polynomial filters and resolve over-smoothing issues.Graph Convolutional Networks (GCNs) are powerful deep learning models for graph-structured data, but they often suffer from over-smoothing, leading to shallow models that struggle to extract high-order information. This paper addresses the over-smoothing problem by proposing GCNII, an extension of the vanilla GCN model with two techniques: Initial Residual and Identity Mapping. These techniques effectively alleviate over-smoothing and enable the model to achieve state-of-the-art performance on various semi-supervised and full-supervised tasks. Theoretical and empirical evidence supports the effectiveness of these techniques, demonstrating that GCNII can express polynomial filters with arbitrary coefficients, thus preventing over-smoothing even in deep networks. Experiments on multiple datasets show that GCNII outperforms existing methods, including deep models like JKNet and DropEdge. The paper also provides a spectral analysis of GCNII, showing that it can express arbitrary polynomial filters and resolve over-smoothing issues.