Boolean Matrix Representation of Graph

A relation R or graph on a finite set can be expressed as a boolean matrix M where:

M[i, j] = 1 iff (i, j) ∈ R .

Multiplication of boolean matrices is done in the same way as ordinary matrix multiplication, but using ∧ for · and ∨ for + .

Property:	Matrix:
Identity, R0	In (identity matrix)
Inverse, R-1 or Γ-1	MT
Reflexive	I ⊆ M
Symmetric	M = MT
Transitive	M2 ⊆ M
Antisymmetric	M ∩ MT ⊆ In
Paths of length n	Mn
Transitive closure Γ+	∪i=1n Mi
Reflexive transitive closure Γ*	∪i=0n Mi

Example: Let the set S be basic blocks of a program and Γ be transfers of control between blocks.