The height of a tree 
is defined as the vertex height
of its root vertex, where the vertex
height of a vertex 
in a tree 
is the number of edges on the longest downward path between
and a tree leaf.
A function to return the height of a vertex 
in a tree 
may be implemented in a future version of the Wolfram
Language as TreeHeight[g, v], and a function to return
the height of a tree as TreeHeight[g].
See also
Root Vertex, Rooted Tree, Tree, Tree Leaf
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Cite this as:
Weisstein, Eric W. "Tree Height." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TreeHeight.html