and provide an insight into the interdependence between f and g, and their effects on solubility. We plot the empirical densities of this quantity for the whole data and the two fragments in Figure . Among the two data subgroups, we observe the density for the > median MolWt is right-shifted compared to the < median MolWt. The density plot of the combined data also exhibits multimodality. This suggests clear differences in the relative contributions of graph and chemical features in explaining solubility between the two data fragments. To investigate it further, in Figure , we illustrate C f,g , values for a selection of molecules from the data. Summarizing from C f,g values we observe the molecules primarily form 'C f,g negative and away from zero', 'C f,g negative and nearzero', 'C f,g positive and near-zero', and 'C f,g positive and away from zero' groups respectively. The near-zero C f,g as enlisted in Figure (a) are shown to posses both branched as well as subfragments comprising of heavy elements and double bonds. And this also includes cases where the compound is heteronuclear for e.g. molecule 5 in Figure (a). In Figure (b) molecules that are primarily agglomerate salts such as molecules 6,10,11,12 and 14 form the cases where 'C f,g negative and away from zero', while molecules 2 and 7 fall under category 'C f,g negative and close to zero'. Again, small branched molecules such molecules 1,13,15 and 16 form category 'C f,g positive and away from zero' as compared to molecule 3,4,8 and 9 form 'C f,g positive and near-zero'. Our analysis using a nonparametric additive characterization indicates that solubilities of smaller, connected molecules tend to depend more on graph-based predictors like weighted adjacency matrix, node importance, and other centrality measures in comparison to the agglomerates or salt-like compounds, which form disjointed graphs.