Structural and chemical properties of the small water clusters W-4, W-5 and W-6 are investigated with the theory of atoms and molecules (QTAIM). For the W-4, W-5 and W-6 clusters, nine, fourteen and twenty-seven conformers, respectively, have been analyzed. For the W-4, W-5 and W-6 clusters one, two and three of these structures, respectively, have not been reported before. We then proceed to extend the W-4, W-5 and W-6 water cluster topology space using QTAIM; the Poincare-Hopf topological sum rules are applied to create rules to identify the spanning set of conformer topologies, this includes finding three, ten and eight new distinct topologies that satisfy the Poincare-Hopf relation for W-4, W-5 and W-6 respectively. The topological stability of degenerate solutions to the Poincare-Hopf relation is compared by evaluating the proximity to rupturing of critical points of the gradient vector field of the charge density. We introduce a QTAIM topology space to replace the inconsistent use of Euclidean geometry to determine whether a cluster is 1-, 2- or 3-D. We show from the topology of the charge density that the conformers of the W-4, W-5 clusters are more energetically stable in less compact, planar forms, conversely the conformers of W-6 are more energetically stable with compact 3-D topologies. Quantifying the degree of covalent character in the hydrogen bonding for the W-4, W-5 and W-6 clusters independently verifies this finding. Differences in simple rules for the number of hydrogen bonds obeying the Bernal-Fowler ice rules between W-4, W-5 and W-6 reflect the transition from 2-D to 3-D structures being more energetically stable. In addition, we identify a new class of O-O bonding interactions that are up to 48% longer than the inter-nuclear separation and appear to be failed hydrogen bonds.