Centroid — центроид.
A branch of a tree at a vertex is a maximal subtree of , in which the degree of is unity. Therefore, the number of branches at is . The branch-weight centroid number of a vertex in a tree , denoted by is the the maximum size of any branch at . A vertex of a tree is a centroid vertex of if has minimum branch-weight centroid number. The centroid of consists of its set of centroid vertices. Jordan (1869) has proved the following theorem.
Theorem. The centroid of a tree consists of either a single vertex or a pair of adjacent vertices.
- Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009.