To reduce storage and computational cost for processing and visualizing large-scale 3D point clouds, an efficient resampling strategy is needed to select a representative subset of 3D points that can preserve contours in the original 3D point cloud. We tackle this problem by using graph-based techniques as graphs can represent underlying surfaces and lend themselves well to efficient computation. We first construct a general graph for a 3D point cloud and then propose a graph-based metric to quantify the contour information via high-pass graph filtering. Finally, we obtain an optimal resampling distribution that preserves the contour information by solving an optimization problem. When browsing, the proposed graph-based resampling performs better than uniform resampling both for toy point clouds as well as real large-scale point clouds. Furthermore, as neither mesh construction nor surface normal calculation is involved, the proposed graph-based method is computationally more efficient than the mesh-based methods.