  We consider the question of determining whether a given group (especially one
generated by involutions) is a right-angled Coxeter group. We describe a group
invariant, the involution graph, and we characterize the involution graphs of
right-angled Coxeter groups. We use this characterization to describe a process
for constructing candidate right-angled Coxeter presentations for a given group
or proving that one cannot exist. We provide some first applications. In
addition, we provide an elementary proof of rigidity of the defining graph for
a right-angled Coxeter group. We also recover a result stating that if the
defining graph contains no SILs, then Aut^0(W) is a right-angled Coxeter group.
