The matrix norm distance (Eq. 25) of the covariance matrices of randomly generated, minimally connected graphs to the covariance matrix of the full design with all 𝑛 choose 2 edges, 𝐂 𝑓 𝑢𝑙𝑙 . The weights used were randomly generated for each value of 𝑛 and then held constant when varying 𝑘. We repeated data collection 20 times for each combination of 𝑛 and 𝑘. The shaded regions show the standard deviation of the distances. The integer edge number, 𝑘, nearest to 𝑛 ⋅ ln(𝑛) is shown with a black circular marker.