In the limit where it is feasible to perform all alchemical transformations accurately, we would like to plan our perturbation map so that 𝑘 approximates the full design with all possible edges, 𝒢 (𝑛, 𝑘 𝑓 𝑢𝑙𝑙 ). Two objects could be considered similar if they are close in distance to each other. If entries in arrays are farther in magnitude, two arrays are distant from each other and vice versa. But, objects such as vectors and matrices must have their lengths defined using a norm. To measure how different a design is from the the full design, we therefore calculate the matrix norm distance between the covariance matrix of the full design, 𝐂 𝑓 𝑢𝑙𝑙 , and the covariance matrices of randomly generated graphs at varied 𝑘, 𝐂 𝑖 . We use the Frobenius norm to calculate distances (Methods and Materials, Eq. 25). To perform this analysis, we measure the distance to 𝐂 𝑓 𝑢𝑙𝑙 for designs with varied edge count and with 10, 20, and 40 ligands. We find that as 𝑘 decreases, 𝐂 𝑖 becomes increasingly further from 𝐂 𝑓 𝑢𝑙𝑙 (Fig. ). The magnitude of the difference increases for designs with more ligands (Fig. ). We also find that the first and second moments in the matrix norm distance monotonically converge towards 𝐂 𝑓 𝑢𝑙𝑙 as 𝑘 approaches 𝑘 𝑓 𝑢𝑙𝑙 (Fig. ). The rapid and monotonic decrease in the second moment of the matrix norm distance with increasing 𝑘 means that the expected variability is inversely related to 𝑘. Further, once designs have on average 𝑛 ln(𝑛) edges, 𝐂 𝑖 starts to plateau towards 𝐂 𝑓 𝑢𝑙𝑙 (Fig. ), suggesting that designs with 𝑛 ln(𝑛) edges reasonably approximate 𝒢 (𝑛, 𝑘 𝑓 𝑢𝑙𝑙 ).