This paper proposes a deep learning approach for parameterizing an unorganized or scattered point cloud in R 3 with graph convolutional neural networks. It builds upon a graph convolutional neural network that predicts the weights (called parameterization weights) of certain convex combinations that lead to a mapping of the 3D points into a planar parameter domain. First, we compute a radius neighbours graph that yields proximity information to each 3D point in the cloud. This radius graph is then converted to its line graph, which encodes edge adjacencies, and is equipped with appropriate weights. The line graph is used as input to a graph convolutional neural network trained to predict optimal parameterizations. The proposed model outperforms closed-form choices of the parameterization weights and produces high quality parameterizations for surface reconstruction schemes.