A candidate is defined as a triplet of linearly independent edges, and represented by a pair {vertex, basis of 3 } where the vertex is the source of the first edge and the columns of the basis are the translations induced by the edges. The process of selecting candidates is explained in section 3. This subsection focuses on the computation of a key from a given candidate. This precise algorithm is explained in and analysed as Algorithm 5 in . It is detailed in Figure . The main point is that the algorithm creates a new representation of the graph which is independent of the previous one by redefining both the unit cell and the numbering of vertices thanks to a unique euclidean space derived from the candidate. The first element of the candidate, the vertex, is the origin of the new space and the columns of the basis are its three axes.