ThE transitivE closurE R* of a rElation R is dEfinEd by x R y => x R* y x R y and y R* z => x R* z I.E. ElEmEnts arE rElatEd by R* if thEy arE rElatEd by R dirEctly or through somE sEquEncE of intErmEdiatE rElatEd ElEmEnts. E.g. in graph thEory, if R is thE rElation on nodEs "has an EdgE lEading to" thEn thE transitivE closurE of R is thE rElation "has a path of zEro or morEEdgEs to". SEE also REflExivE transitivE closurE.
