Finding structure-preserving correspondences between pairs of shapes is a common operation in many geometry processing and applications. Usually the ambiguity of primary correspondences and symmetrical correspondences arises in the matching problem between two intrinsically symmetrical shapes. As intrinsically symmetrical shapes are ubiquitous, it is essential to handle this problem. In this paper, we present an approach to establish automatic sparse symmetry-aware correspondences between two shapes using graph matching. We propose a directed-angle scheme to capture the global structure of meshes. Then the graph matching is generalized to high-order potentials, which contains intrinsic descriptors, intrinsic distances and directed-angles among arbitrary three points in deformation-invariant embedding space of the mesh. Comprehensive experiments demonstrate that our method works well.