  Given a finite simplicial graph ${\cal G}$, the graph group $G{\cal G}$" is
the group with generators in one-to-one correspondence with the vertices of
${\cal G}$ and with relations stating two generators commute if their
associated vertices are adjacent in ${\cal G}$. The Bieri-Neumann-Strebel
invariant can be explicitly described in terms of the original graph ${\cal G}$
and hence there is an explicit description of the distribution of finitely
generated normal subgroups of $G{\cal G}$ with abelian quotient. We construct
Eilenberg-MacLane spaces for graph groups and find partial extensions of this
work to the higher dimensional invariants.
