  We investigate a construction which associates a finite von Neumann algebra
$M(\Gamma,\mu)$ to a finite weighted graph $(\Gamma,\mu)$. Pleasantly, but not
surprisingly, the von Neumann algebra associated to to a `flower with $n$
petals' is the group von Neumann algebra of the free group on $n$ generators.
In general, the algebra $M(\Gamma,\mu)$ is a free product, with amalgamation
over a finite-dimensional abelian subalgebra corresponding to the vertex set,
of algebras associated to subgraphs `with one edge' (or actually a pair of dual
edges). This also yields `natural' examples of (i) a Fock-type model of an
operator with a free Poisson distribution; and (ii) $\C \oplus \C$-valued
circular and semi-circular operators.
