This paper introduces Edge-Conditioned Convolution (ECC), a novel convolution operation on graph signals performed in the spatial domain where filter weights are conditioned on edge labels and dynamically generated for each specific input sample. ECC generalizes standard convolution on graphs by leveraging edge labels, which allows for more accurate and flexible graph processing. The method is applied to both point clouds and general graphs, achieving state-of-the-art performance on several benchmark datasets. ECC is designed to handle graphs with varying sizes and structures, and it uses edge labels to condition filter weights, enabling more effective local neighborhood processing. This approach is particularly effective for point cloud classification, where it outperforms existing methods on the Sydney dataset. Additionally, ECC achieves competitive performance on graph classification tasks, including the NCI1 dataset, where it outperforms other deep learning approaches. The method is evaluated on various tasks, including point cloud classification, graph classification, and MNIST digit recognition. On the MNIST dataset, ECC achieves performance comparable to standard convolutional networks, demonstrating its effectiveness in both regular and irregular data settings. The results show that ECC can retain the same number of parameters and computational complexity as regular convolution on grids, while also benefiting from edge label information. The paper also discusses the application of ECC to general graphs, where it is shown to be effective in tasks such as chemical compound classification and enzyme structure recognition. The method is robust to noise and can be adapted to different graph structures, making it a versatile tool for graph-based learning tasks. Overall, ECC provides a flexible and effective approach to graph convolution, with potential applications in a wide range of domains.This paper introduces Edge-Conditioned Convolution (ECC), a novel convolution operation on graph signals performed in the spatial domain where filter weights are conditioned on edge labels and dynamically generated for each specific input sample. ECC generalizes standard convolution on graphs by leveraging edge labels, which allows for more accurate and flexible graph processing. The method is applied to both point clouds and general graphs, achieving state-of-the-art performance on several benchmark datasets. ECC is designed to handle graphs with varying sizes and structures, and it uses edge labels to condition filter weights, enabling more effective local neighborhood processing. This approach is particularly effective for point cloud classification, where it outperforms existing methods on the Sydney dataset. Additionally, ECC achieves competitive performance on graph classification tasks, including the NCI1 dataset, where it outperforms other deep learning approaches. The method is evaluated on various tasks, including point cloud classification, graph classification, and MNIST digit recognition. On the MNIST dataset, ECC achieves performance comparable to standard convolutional networks, demonstrating its effectiveness in both regular and irregular data settings. The results show that ECC can retain the same number of parameters and computational complexity as regular convolution on grids, while also benefiting from edge label information. The paper also discusses the application of ECC to general graphs, where it is shown to be effective in tasks such as chemical compound classification and enzyme structure recognition. The method is robust to noise and can be adapted to different graph structures, making it a versatile tool for graph-based learning tasks. Overall, ECC provides a flexible and effective approach to graph convolution, with potential applications in a wide range of domains.