Deep Neural Networks have achieved impressive performance on computer vision tasks such as classification, localization, segmentation, captioning, and generation. Applying the same techniques to 3D point clouds requires a different approach, because they are not aligned along a grid that a fixed-size kernel can slide across. We propose treating these point clouds as graphs with connections between nearest neighbors. With this structure we can define a graph convolution with a fixed-size kernel that can handle variable-size neighborhoods as well as an algebraic graph pooling o peration based on graph clustering. With these operations we build convolutional neural networks for 3D object classification on the ModelNet dataset, achieving results comparable to the state of the art. We also discuss how sparse implementations of these operations reduce their memory and computational complexity.