A tree to whose nodes and/or edges labels (usually number)
are assigned.

The word "weight" also has a more specific meaning when applied to trees, namely the weight of a tree at a point is the maximum number of edges in any branch
at (Harary 1994, p. 35), as illustrated
above. A point having minimal weight for the tree is called a centroid
point, and the tree centroid is the set of all
centroid points.