Transitive closure is a concept from graph theory, specifically related to directed graphs (digraphs) or relations. Essentially, the transitive closure of a directed graph is a new graph that contains the same vertices as the original graph, with additional edges that represent the transitive relations between those vertices.
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The transitive closure is the least transitive set containing every member of . It is obtained by taking the union of all finite iterates of the union operation starting from . This set-theoretic construction uses the membership binary relation; transitive closure of a relation instead closes an arbitrary binary relation under composition.