Connectivity information for an arbitrary surface structure is difficult to obtain accurately using conventional techniques. Methods involving cutoff radii rely upon absolute distances which have difficulty accounting for changes in atomic spacing in mixed chemical environments, such as alloys. In these systems, lattice constants can change significantly, requiring species dependent atomic radii which are difficult, if not impossible, to tune correctly for all possible bulk systems. Methods based on relative distances, i.e. "space filling" techniques such as Voronoi tessellation, 9 perform well in bulk environments, but are not robust for surface terminations. For this reason, it is important to begin the surface enumeration process from a provided bulk structure. From the bulk, connectivity can be determined using Voronoi tessellation, or similar methodology. Once the connectivity of the bulk's structure has been determined within a 3D periodic system, it can be utilized to obtain the surface terminated atoms and the slab's connectivity graph. This is done by taking the unit cell of the slab before it has been cleaved and repeating it once in the basis vector perpendicular to the normal of the Miller plane. This results in a slab twice the width. This is depicted in Figure for a (100) cleave of a simple cubic system, where bulk atoms have a total connectivity of 6. By breaking the connectivity matrix of the supercell into 4 equal quadrants, the corresponding surface connectivity can be interpreted as either of the symmetrically equivalent quadrants along the diagonal.