The eccentricity of a node is the maximum distance from that node to any other node. The radius of a tree is the minimum eccentricity across all nodes.
The center of a tree has eccentricity equal to the radius. The diameter equals when even, or when odd.
These terms appear in graph theory and can help verify your diameter calculations. If your center's eccentricity differs from half the diameter by more than one, something is wrong.