Various embodiments include techniques for generating topological data for a mesh included in a computer-generated environment. The mesh includes simple geometric shapes, such as triangles. The disclosed techniques identify vertices in the mesh that have the same position and have identical attributes, such as color, normal vector, and texture coordinates. The disclosed techniques further identify vertices in the mesh that have the same position but differ in one or more attributes. The techniques generate lists of the triangles that are adjacent to each vertex included in the mesh. The techniques generate a list of the unique edges included in the mesh. Further, the techniques are well suited for execution on highly parallel processors, such as graphics processing units, thereby reducing the time to generate this topological data. The topological data may then be efficiently used by other computer graphics processing operations.