n. 1. also called tree diagram. (Graph theory) a connected graph of which the diagram is tree-shaped in that there are no loops or paths leading from any vertex back to itself. It is a rooted tree if one vertex is distinguished as the root or origin, as in the figure below; otherwise it is a free tree; in a labelled tree, a unique element is associated with each node. A finite set of node-disjoint trees comprises a forest.
A rooted tree. 2. a compact connected set in which every pair of points is joined by a unique rectifiable path.