A weighted tree is a tree to whose nodes and/or edges labels (usually numbers) 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.
