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

Note:

The Levenshtein distance (or edit distance) is between two strings

But in Graph you should search between at least N! position that you find Identity of each edge and vertex. You can compare between two graph by unique index easily,But The master question is define identity for each vertex and edge.this question (find identity for each vertex and edge in two graph that they can to transform ) is very hard and was called isomorphism problem (NP-Complete). You can search about isomorphism graph.