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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]
At the same time, isomorphism for many special classes of graphs can be solved in polynomial time, and in practice graph isomorphism can often be solved efficiently. [ 3 ] [ 4 ] This problem is a special case of the subgraph isomorphism problem , [ 5 ] which asks whether a given graph G contains a subgraph that is isomorphic to another given ...
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]
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.
Weisfeiler, an experienced outdoorsman, flew to Chile at Christmas time of 1984 to hike alone in the Chilean Andes. Chile was then under a military dictatorship headed by General Augusto Pinochet, which committed numerous human rights abuses (before he died in 2006, Pinochet had been prosecuted for his role in Operation Colombo and indicted in absentia in other countries).
Subgraph isomorphism is a generalization of both the maximum clique problem and the problem of testing whether a graph contains a Hamiltonian cycle, and is therefore NP-complete. [1] However certain other cases of subgraph isomorphism may be solved in polynomial time. [2] Sometimes the name subgraph matching is also used for the same problem ...