We introduce an Alexander polynomial for MOY graphs. For a framed trivalent MOY
graph G, we refine the construction and obtain a framed ambient isotopy invariant
\Delta(G,c)(t). The invariant \Delta(G,c)(t) satisfies a series of relations, which we call MOY type relations, and conversely these relations determine \Delta(G,c)(t). Using them we
provide a graphical definition of the Alexander polynomial of a link. Finally, we
discuss some properties and applications of our invariants.