Abstract: We construct and classify self-adjoint realisations of the Dirac operator on a compact, metric graph and discuss circumstances under which chiral symmetry is realised. We then establish some spectral properties. Extending the quantum graph models to include a time variable, we introduce a coupling to abelian gauge fields. In these extended models we establish self-adjointness and chiral symmetry, and discuss some spectral properties. We finally approach an index theorem that serves as an important input for a Schwinger model on a graph.