  We consider the setting of Reeb graphs of piecewise linear functions and
study distances between them that are stable, meaning that functions which are
similar in the supremum norm ought to have similar Reeb graphs. We define an
edit distance for Reeb graphs and prove that it is stable and universal,
meaning that it provides an upper bound to any other stable distance. In
contrast, via a specific construction, we show that the interleaving distance
and the functional distortion distance on Reeb graphs are not universal.
