We consider four common defects that appear in an infinite single-layer graphene lattice, i.e. single vacancy V₁(5-9), Stone-Wales SW (55-77), and double vacancies V₂(5-8-5) and V₂(555-777). Investigating the honeycomb pattern of the graphene, we make use of the concept of shortest closed paths (periodic orbits) in the underlying topological structure. Using properties of the shortest closed paths of odd length we present and prove mathematically an algorithm that classifies which one of these defects occurs. © 2023 Taylor & Francis Group, LLC.