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) &isin R .

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

Property: Matrix:
Identity, R0 In (identity matrix)
Inverse, R-1 or &Gamma-1 MT
Reflexive I &sube M
Symmetric M = MT
Transitive M2 &sube M
Antisymmetric M &cap MT &sube In
Paths of length n Mn
Transitive closure &Gamma+ &cupi=1n Mi
Reflexive transitive closure &Gamma* &cupi=0n Mi

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

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