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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.