Edit distance between two graphs

Question

I\'m just wondering if, like for strings where we have the Levenshtein distance (or edit distance) between two strings, is there something similar for graphs?

I mean

Answer 1

For a general graph it is a NP-complete problem as others mentioned in their answer. But for tree graph there are well known polynomial algorithms. May be most famous of them is "Zhang Shasha" algorithm which was published in 1989.