This paper follows cognitive studies to investigate a graph representation for sketches, where the information of strokes, i.e., parts of a sketch, are encoded on vertices and information of inter-stroke on edges. The resultant graph representation facilitates the training of a Graph Neural Networks for classification tasks, and achieves accuracy and robustness comparable to the state-of-the-art against translation and rotation attacks, as well as stronger attacks on graph vertices and topologies, i.e., modifications and addition of strokes, all without resorting to adversarial training. Prior studies on sketches, e.g., graph transformers, encode control points of stroke on vertices, which are not invariant to spatial transformations. In contrary, we encode vertices and edges using pairwise distances among control points to achieve invariance. Compared with existing generative sketch model for one-shot classification , our method does not rely on run-time statistical inference. Lastly, the proposed representation enables generation of novel sketches that are structurally similar to while separable from the existing dataset.