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In graph theory, the Weisfeiler Leman graph isomorphism test is a heuristic test for the existence of an isomorphism between two graphs G and H. [1] It is a generalization of the color refinement algorithm and has been first described by Weisfeiler and Leman in 1968. [ 2 ]
In graph theory and theoretical computer science, the colour refinement algorithm also known as the naive vertex classification, or the 1-dimensional version of the Weisfeiler-Leman algorithm, is a routine used for testing whether two graphs are isomorphic. [1]
Attempt to construct an isomorphism using P as subroutine. Mark a vertex u in G and v in H, and modify the graphs to make them distinctive (with a small local change). Ask P if the modified graphs are isomorphic. If no, change v to a different vertex. Continue searching. Either the isomorphism will be found (and can be verified), or P will ...
The Weisfeiler Leman graph isomorphism test can be used to heuristically test for graph isomorphism. [14] If the test fails the two input graphs are guaranteed to be non-isomorphic. If the test succeeds the graphs may or may not be isomorphic. There are generalizations of the test algorithm that are guaranteed to detect isomorphisms, however ...
Andrey Aleksandrovich Leman (Russian: Андрей Александрович Леман, 1940–2012) was a Soviet mathematician and computer scientist who is known for the development of the Weisfeiler Leman graph isomorphism test together with Boris Weisfeiler published in 1968. [1]
The graph isomorphism problem is the computational problem of determining whether two finite graphs are isomorphic. Clearly, the graph canonization problem is at least as computationally hard as the graph isomorphism problem. In fact, graph isomorphism is even AC 0-reducible to graph canonization.
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Another examples is the Weisfeiler-Leman graph kernel [9] which computes multiple rounds of the Weisfeiler-Leman algorithm and then computes the similarity of two graphs as the inner product of the histogram vectors of both graphs. In those histogram vectors the kernel collects the number of times a color occurs in the graph in every iteration.