  Given a finite graph G there is a corresponding group given by the
presentation with generators the vertices of G and a relation [x,y]=1 for
generators x and y precisely when (x,y) is an edge of G. Such groups are known
as partially commutative groups (or right-angled Artin groups). In this paper
we construct orthogonality theory for graphs with the study of partially
commutative groups in mind. The theory developed here provides tools for the
study of the structure of the centraliser lattice of partially commutative
groups and for their automorphism groups.
