The critical tree is inherently acyclic (as it is a subgraph of the maximum spanning tree) -a direct consequence of the definition of a critical path. However, it is possible that there are multiple paths with very similar critical values between a given pair of local maxima. For example, the electronic charge density of a benzene molecule exhibits local maxima at the nuclei which can be linked together by traversing the aromatic ring either clockwise, or anticlockwise (see Fig. ). Both of these routes have very similar critical values, but only one (that which has the slightly larger critical value within a finite precision computation) will be included in the critical tree. For the benzene system this means that whichever bond happens to have the lowest electron density will be excluded from the maximum spanning tree, and hence also from the critical tree. However, such bonds can be re-introduced by considering neighbouring basins of attraction, using the following gap-filling algorithm (this produces a critical network according to the definition of Bader ):