On a relation between graph edit distance and maximum common subgraph

In approximate, or error-correcting, graph matching one considers a set of graph edit operations, and defines the edit distance of two graphs g(1) and g(2) as the shortest (or least cost) sequence of edit operations that transform g(1) into g(2). A maximum common subgraph of two graphs g(1) and g(2) is a subgraph of both g(1) and g(2) such that there is no other subgraph of g(1) and g(2) with more nodes. Graph edit distance and maximum common subgraph are well known concepts that have various applications in pattern recognition and machine vision. In this paper a particular cost function for graph edit distance is introduced, and it is shown that under this cost function graph edit distance computation is equivalent to the maximum common subgraph problem. (C) 1997 Elsevier Science B.V.