A detailed analysis concerning the effect of the exchange-correlation functional on a prototypical agostic niobium complex has been carried out, with particular attention to a fundamental property of the functional, namely, the recovering of the uniform electron gas limit. The obtained results allow for revisiting the role of this limit for a proper description of the beta-H agostic interaction. Starting from these results, a new criterion for the bond analysis based on the electron density behavior is proposed. Indeed, the density homogeneity between the metal and the involved hydrogen has been evaluated at the bond critical point, as defined in the framework of Bader's atoms in molecules theory, by calculating the average variation rates of the (reduced) density gradients. Such descriptors not only provide useful insights on the nature of such an interaction but also could be used as a starting point for a deep (and new) analysis of the chemical bond