A novel set of molecular descriptors called SHED (SHannon Entropy Descriptors) is presented. They are derived from distributions of atom-centered feature pairs extracted directly from the topology of molecules. The value of a SHED is then obtained by applying the information-theoretical concept of Shannon entropy to quantify the variability in a feature-pair distribution. The collection of SHED values reflecting the overall distribution of pharmacophoric features in a molecule constitutes its SHED profile. Similarity between pairs of molecules is then assessed by calculating the Euclidean distance of their SHED profiles. Under the assumption that molecules having similar pharmacological profiles should contain similar features distributed in a similar manner, examples are given to show the ability of SHED for scaffold hopping in virtual chemical screening and pharmacological profiling compared to that of substructural BCI fingerprints and three-dimensional GRIND descriptors.