Fig. 2

a Subset of a graphene-like structure in a hexagonal lattice (for the present example, the lattice is assumed to continue outside the drawn boundary). b Three rotationally equivalent seven-sided cycles indicating atoms in defect-free regions. Atomic columns inside such cycles are indicated in blue. c Optimal (nine-sided) and restricted (seven-sided) cycles for atomic columns that are second-nearest neighbor to a vacancy (indicated in purple). d Third-nearest neighbor atomic columns retain the original cycle with loss of rotational symmetry. e Atomic columns adjacent to the vacancy site are described by an eight-sided cycle (indicated in orange). f Final cycle-based color coding of the observed atomic columns based on the algorithm