  We compute the cohomology ring of a generalised type of configuration space
of points in $\mathbb{R}^r$. This configuration space is indexed by a graph. In
the case the graph is complete the result is known and it is due to Arnold and
Cohen. However, our computations give a generalisation to any graph and an
alternative proof of the classical result. Moreover, we show that there are
deletion-contraction short exact sequences for this cohomology rings.
