  We define branching systems for finitely aligned higher-rank graphs. From
these we construct concrete representations of higher-rank graph C*-algebras on
Hilbert spaces. We prove a generalized Cuntz-Krieger uniqueness theorem for
periodic single-vertex 2-graphs. We use this result to give a sufficient
condition under which representations of periodic single-vertex 2-graph
C*-algebras arising from branching systems are faithful.
