The paper introduces a novel neural network architecture, Deep Graph Convolutional Neural Network (DGCNN), designed for graph classification. DGCNN addresses the challenges of extracting meaningful features from graphs and ensuring a consistent ordering of vertices. It features a localized graph convolution layer and a SortPooling layer, which sorts vertex features in a consistent order, enabling traditional neural networks to be trained on graphs without preprocessing. The SortPooling layer is shown to be effective in retaining more vertex information and learning from the global graph topology. Experimental results on benchmark datasets demonstrate that DGCNN achieves competitive performance with state-of-the-art graph kernels and outperforms other deep learning methods for graph classification. The architecture supports end-to-end gradient-based training and does not require graph transformation into vectors, making it a robust and efficient solution for graph classification tasks.The paper introduces a novel neural network architecture, Deep Graph Convolutional Neural Network (DGCNN), designed for graph classification. DGCNN addresses the challenges of extracting meaningful features from graphs and ensuring a consistent ordering of vertices. It features a localized graph convolution layer and a SortPooling layer, which sorts vertex features in a consistent order, enabling traditional neural networks to be trained on graphs without preprocessing. The SortPooling layer is shown to be effective in retaining more vertex information and learning from the global graph topology. Experimental results on benchmark datasets demonstrate that DGCNN achieves competitive performance with state-of-the-art graph kernels and outperforms other deep learning methods for graph classification. The architecture supports end-to-end gradient-based training and does not require graph transformation into vectors, making it a robust and efficient solution for graph classification tasks.