Unlinked embedded graphs

This paper is a self-contained development of an invariant of graphs embedded in three-dimensional Euclidean space using the Jones polynormal and skein theory. The edges of the graphs do not require framing and the vertices are not required to be rigid. Some examples of the invariant are computed. An unlinked embedded graph is one that contains only trivial knots or links. Examples show that the invariant is sufficiently powerful to distinguish some different unlinked embeddings of the same graph.