[1] Graphs are commonly used to encode structural information in many fields, including computer vision and pattern recognition, and graph matching is an important tool in these areas.
For example, in image recognition applications, the results of image segmentation in image processing typically produces data graphs with the numbers of vertices much larger than in the model graphs data expected to match against.
In the case of attributed graphs, even if the numbers of vertices and edges are the same, the matching still may be only inexact.
[1] Two categories of search methods are the ones based on identification of possible and impossible pairings of vertices between the two graphs and methods that formulate graph matching as an optimization problem.
[4][5] The class of algorithms is called error-tolerant graph matching.