<p>Graphene nanostructures (GNSs) exhibit unique electronic and magnetic properties dependent on their shape and size. This research investigates the face index, a topological descriptor derived from chemical graph theory, as a means to characterize the structural topology of three distinct regular convex polygons: triangles, hexagonal, and rhombus-shaped GNSs, which are the most simple high-symmetry convex structures that can be ideally cut out of a graphene layer. We calculate the face index for these three geometries using graph theoretical methods. The results offer quantitative insights into the structure of these nanomaterials and provide a valuable contribution toward understanding structure–property relationships in graphene-based systems.</p>