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This paper formulates a necessary and sufficient condition for a genericgraph matching problem to be equivalent to the maximum vertex and edge weightclique problem in a derived association graph. The consequences of this resultsare threefold: first, the condition is general enough to cover a broad range ofpractical graph matching problems; second, a proof to establish equivalencebetween graph matching and clique search reduces to showing that a given graphmatching problem satisfies the proposed condition; and third, the result setsthe scene for generic continuous solutions for a broad range of graph matchingproblems. To illustrate the mathematical framework, we apply it to a number ofgraph matching problems, including the problem of determining the graph editdistance.

A Necessary and Sufficient Condition for Graph Matching Being Equivalent to the Maximum Weight Clique Problem