Graph Matching & AI

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. In these areas, it is commonly assumed that the comparison is between the data graph and the model graph

Graph Matching - Types

Exact Graph Matching

graph isomorphism problem - the problem of exactly matching a graph to another graph
subgraph isomorphism problem - the problem of exactly matching a graph to a part of another graph

Inexact Graph Matching

The inexact graph matching refers to matching problems when exact matching is impossible, e.g., when the number of vertices in the two graphs are different. In this case, it is required to find the best possible match. For example, in image recognition applications, the results of image segmentation in image processing typically produce 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 maybe only inexact.

Two categories of search methods are the ones based on the identification of possible and impossible pairings of vertices between the two graphs and methods which formulate graph matching as an optimization problem. Graph edit distance is one of the similarity measures suggested for graph matching. The class of algorithms is called error-tolerant graph matching.

Graph Matching - Resources