We hereby introduce the atomic degree of interaction (DOI), a new concept rooted in the electron density-based independent gradient model (IGM). Capturing any manifestation of electron density sharing around an atom, including covalent and non-covalent situations, this index reflects the attachment strength of an atom to its molecular neighbourhood. It is shown to be very sensitive to the local chemical environment of the atom. No significant correlation could be found between the atomic DOI and various other atomic properties, making this index a specific source of information. However, examining the simple H₂ + H reacting system, a strong connection has been established between this electron density-based index and the scalar reaction path curvature, the cornerstone of the benchmark unified reaction valley approach (URVA). We observe that reaction path curvature peaks appear when atoms experience an acceleration phase of electron density sharing during the reaction, detected by peaks of the DOI second derivative either in the forward or reverse direction. This new IGM-DOI tool is only in its early stages, but it opens the way to an atomic-level interpretation of reaction phases. More generally, the IGM-DOI tool may also serve as an atomic probe of electronic structure changes of a molecule under the influence of physicochemical perturbations.