This paper addresses the challenge of representation learning for graph data, particularly in the context of node classification and graph classification tasks. Traditional convolutional neural networks (CNNs) are well-suited for image data but struggle with graph data due to the lack of spatial locality and order information in graphs. To bridge this gap, the authors propose novel graph pooling (gPool) and unpooling (gUnpool) operations. gPool adaptively selects a subset of nodes based on their scalar projection values onto a trainable projection vector, while gUnpool restores the graph to its original structure using the position information of the selected nodes. These operations form the basis of the graph U-Nets (g-U-Nets), an encoder-decoder architecture designed for graph data. Experimental results on various datasets demonstrate that g-U-Nets achieve superior performance compared to previous methods, highlighting the effectiveness of the proposed graph pooling and unpooling operations. The paper also discusses the importance of graph connectivity augmentation and the impact of network depth on performance.This paper addresses the challenge of representation learning for graph data, particularly in the context of node classification and graph classification tasks. Traditional convolutional neural networks (CNNs) are well-suited for image data but struggle with graph data due to the lack of spatial locality and order information in graphs. To bridge this gap, the authors propose novel graph pooling (gPool) and unpooling (gUnpool) operations. gPool adaptively selects a subset of nodes based on their scalar projection values onto a trainable projection vector, while gUnpool restores the graph to its original structure using the position information of the selected nodes. These operations form the basis of the graph U-Nets (g-U-Nets), an encoder-decoder architecture designed for graph data. Experimental results on various datasets demonstrate that g-U-Nets achieve superior performance compared to previous methods, highlighting the effectiveness of the proposed graph pooling and unpooling operations. The paper also discusses the importance of graph connectivity augmentation and the impact of network depth on performance.