  In this paper we verify that the graph forms a complete invariant for Banach
algebra isomorphisms of tensor algebras of graphs. For tensor algebras
associated with countable directed graphs having no sinks the graph forms an
invariant for algebraic isomorphisms as well. The graph also forms a complete
invariant for w*-bicontinuous isomorphisms of free semigroupoid algebras. For
free semigroupoid algebras associated with countable directed locally finite
graphs with no sinks, the graph also forms an invariant for algebraic
isomorphisms.
