(iii) Important graphical features: Among the graph attributes, the most important ones are score (score), leverage (lev), and nodal impact (nod imp), albeit only for the higher median molecular weight (> median MolWt) case. We compute these attributes at each node and then take an average. Nodal impact for each node quantifies the impact of each node by measuring the change in average distances in the network upon removal of that node . Leverage centrality at each node is the ratio of the degree of a node to its neighbors, and it thus measures the reliance of its immediate neighbors on that node for information . The score variable is the average of the s-core memberships of the nodes . We see that degree by itself is less important than these measures, when both leverage and score are based on nodal degrees, but also take into account the degrees of the neighboring nodes or atoms. The nodal impact being important also implies the importance of the graphical connectivity profile in explaining solubility.