Deriving from image matching and understanding, semantic keypoint matching aims at establishing correspondence between keypoint sets in images. As graphs are powerful tools to represent points and their complex relationships, graph matching provides an effective way to find desired semantic keypoint correspondences. Recent deep graph matching methods have shown excellent performance, but there is still a lack of exploration and utilization of spatial information of keypoints as nodes in graphs. More specifically, existing methods are insufficient to capture the relative spatial relations through current graph construction approaches from the locations of semantic keypoints. To address these issues, we introduce a positional reconstruction encoder-decoder (PR-EnDec) to model intrinsic graph spatial structure, and present an end-to-end graph matching network PREGM based on PR-EnDec. Our PR-EnDec consists of a positional encoder that learns effective node spatial embedding with the affine transformation invariance, and a spatial relation decoder that further utilizes the high-order spatial information by reconstructing the locational structure of graphs contained in the node coordinates. Extensive experimental results on three public keypoint matching datasets demonstrate the effectiveness of our proposed PREGM.