  We describe a class of $C^*$-algebras which simultaneously generalise the
ultragraph algebras of Tomforde and the shift space $C^*$-algebras of
Matsumoto. In doing so we shed some new light on the different $C^*$-algebras
that may be associated to a shift space. Finally, we show how to associate a
simple $C^*$-algebra to an irreducible sofic shift.
