transitive closure

1 definition found

transitive closure - Free On-line Dictionary of Computing (26 May 2007) :

  transitive closure
  
     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 more edges to".  See also
     Reflexive transitive closure.