Definitions

the “topological gene”

Variants of the BCT string can be used as a “topological gene” description of a tree

adapted from
PLoS supp. material by Hermann Cuntz

← sorted_and_equivalent_tree
→ tree_morphing

Once the labels of a tree are topologically sorted (see “sort_tree”), a unique representation of the topology is given by the topological “gene” (see “gene_tree”):

green segments are branches ending with a branch point, black segments are branches ending with a termination point; the order is determined by the topological sorting described on the previous page. Numbers on the “gene” branches (and also their actual length) correspond to the path length along each branch. In this case the node labels are displayed under the “gene” for descriptive purposes. Apart from the diameter mapping, the equivalent tree can be reconstructed solely from this one-dimensional string.

Because of the continuous labelling sub-trees of the original tree are continuous bits within the topological “gene” (see red contours).