We investigate conditions on a graph C * -algebra for the existence of a faithful semifinite trace. Using such a trace and the natural gauge action of the circle on the graph algebra, we construct a smooth ( 1 , ∞ ) -summable semi-finite spectral triple. The local index theorem allows us to compute the pairing with K-theory. This produces invariants in the K-theory of the fixed point algebra, and these are invariants for a finer structure than the isomorphism class of C * ( E ) .