  The diagram algebra introduced by Brauer that describes the centralizer
algebra on tensor products of the natural representation of an orthogonal group
has a presentation by generators and relations that only depends on the graph
of type An on n nodes. Here we describe an algebra depending on an arbitrary
graph of type M. We study its structure when the type is An, Dn, E6, E7, E8. We
determine the representations and find the dimensions. The algebra is
generically semisimple and contains the group algebra of the Coxeter type M as
a subalgebra. It is a ring homomorphism of the Birman-Murakami-Wenzl algebra of
these types. This fact will be used in later work determining the structure of
Birman-Murakami-Wenzl algebras of simply laced spherical type.
