  For any non-negative integers $v > k > i$, the {\em generalized Johnson
graph}, $J(v,k,i)$, is the undirected simple graph whose vertices are the
$k$-subsets of a $v$-set, and where any two vertices $A$ and $B$ are adjacent
whenever $|A \cap B| =i$. In this article, we derive formulas for the girth,
odd girth, distance function, and diameter of $J(v,k,i)$.
