We study the connections between \emph{graph models} and
\emph{``wave-style'' Geometry of Interaction} (GoI)
$\lambda$-models. The latters arise when Abramsky's GoI
axiomatization, which generalizes Girard's original GoI, is applied to
a traced monoidal category with the \emph{categorical product} as
tensor, using a countable power as the traced strong monoidal
functor~\bang.\ Abramsky hinted that the category $\mathit{Rel}$ of
sets and relations is the basic setting for traditional denotational
``static semantics''.  However, the category $\mathit{Rel}$ together
with the cartesian product apparently escapes original Abramsky's
axiomatization. Here we show that, by moving to the category
$\mathit{Rel}^*$ of \emph{pointed sets} and relations preserving the
distinguished point, and by sligthly relaxing Abramsky's GoI
axiomatization, we can recover a large class of graph-like models as
wave models.  Furthermore, we show that the class of untyped
$\lambda$-theories induced by wave-style GoI models is richer than
that induced by game models. 

\\ {\bf Keywords:} (linear) graph model, traced monoidal category,
weak linear category, categorical geometry of interaction.