  Chern-Simons gauge theory, since its inception as a topological quantum field
theory, has proved to be a rich source of understanding for knot invariants. In
this work the theory is used to explore the definition of the expectation value
of a network of Wilson lines - an embedded graph invariant. Using a slight
generalization of the variational method, lowest-order results for invariants
for arbitrary valence graphs are derived; gauge invariant operators are
introduced; and some higher order results are found. The method used here
provides a Vassiliev-type definition of graph invariants which depend on both
the embedding of the graph and the group structure of the gauge theory. It is
found that one need not frame individual vertices. Though, without a global
projection of the graph, there is an ambiguity in the relation of the
decomposition of distinct vertices. It is suggested that framing may be seen as
arising from this ambiguity - as a way of relating frames at distinct vertices.
