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, a scalar measure that identifies the number of atomic operations (node and edges insertion/deletion) to transform a graph G1 to a graph G2.

Answer 1

I think graph edit distance is the measure that you were looking for.

Graph edit distance measures the minimum number of graph edit operations to transform one graph to another, and the allowed graph edit operations includes:

• Insert/delete an isolated vertex
• Insert/delete an edge
• Change the label of a vertex/edge (if labeled graphs)

However, computing the graph edit distance between two graphs is NP-hard. The most efficient algorithm for computing this is an A*-based algorithm, and there are other sub-optimal algorithms.