  We prove a spectral theorem for bimodules in the context of graph
C*-algebras. A bimodule over a suitable abelian algebra is determined by its
spectrum (i.e., its groupoid partial order) iff it is generated by the
Cuntz-Krieger partial isometries which it contains iff it is invariant under
the gauge automorphisms. We study 1-cocycles on the Cuntz-Krieger groupoid
associated with a graph C*-algebra, obtaining results on when integer valued or
bounded cocycles on the natural AF subgroupoid extend. To a finite graph with a
total order, we associate a nest subalgebra of the graph C*-algebra and then
determine its spectrum. This is used to investigate properties of the nest
subalgebra. We give a characterization of the partial isometries in a graph
C*-algebra which normalize a natural diagonal subalgebra and use this to show
that guage invariant generating triangular subalgebras are classified by their
spectra.
