Atoms in Molecules (AIM) theory is routinely used to assess hydrogen bond formation; however its stringent criteria controversially exclude some systems that otherwise appear to exhibit weak hydrogen bonds. We show that a regional analysis of the reduced density gradient, as provided by the recently introduced Non-Covalent Interactions (NCI) index, transcends AIM theory to deliver a chemically intuitive description of hydrogen bonding for a series of 1,n-alkanediols. This regional definition of interactions overcomes the known caveat of only analyzing electron density critical points. In other words, the NCI approach is a simple and elegant generalization of the bond critical point approach, which raises the title question. Namely, is it the presence of an electron density bond critical point that defines a hydrogen bond or the general topology in the region surrounding it?