A graph with a semiregular group of automorphisms can be thought of as the
derived cover arising from a voltage graph. Since its inception, the theory of
voltage graphs and their derived covers has been a powerful tool used in the
study of graphs with a significant degree of symmetry. We generalise this
theory to graphs with a group of automorphisms that is not necessarily
semiregular, and we generalise several well-known results of the classical
theory of voltage graphs to this broader setting