The derivation leading to Eq. 13 clarifies what number of edges are likely to produce minimally connected designs, but it does not yet address how connectivity changes for minimally connected designs. The gradual shift in eigenspectra of ℱ for minimally connected designs (Fig. ) is related to shifts in connectivity . An example of a weakly connected design could be a design with only one perturbation per ligand, no cycles, and more edges on average separating ligands. For a weakly connected, weighted design, edges could also have low weights.