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 u is the maximum number of edges in any branch at u, 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.

centroid point | labeled graph | Taylor's condition | tree | tree centroid | weighted graph