To address the issue of the inadequate structural representation capability of hand-drawn sketches represented by simple graphs, we propose a sketch composition method called Directed Sequential Sketch Graph. This method introduces temporal information into sketch graphs, enabling graph neural networks to consider both the topological and temporal structures of sketches. Unlike previous methods that use the original sequence data of sketches, DSSG is a novel sketch representation based on graph data. While directly constructing sketch sequences as simple graphs only includes the topological structure of sketches, DSSG reconstructs the simple graph of a sketch to obtain a graph data sketch with temporal structure. We compared the classification performance of the simple graph method and the DSSG method on the QuickDraw dataset. The accuracy of DSSG on various graph convolutional networks improved by 1.39–31.84% compared to the simple graph method, demonstrating the feasibility and effectiveness of our sketch composition method.