  We investigate the ideal structures of the C^*-algebras arising from
topological graphs. We give the complete description of ideals of such
C^*-algebras which are invariant under the so-called gauge action, and give the
condition on topological graphs so that all ideals are invariant under the
gauge action. We get conditions for our C^*-algebras to be simple, prime or
primitive. We completely determine the prime ideals, and show that most of them
are primitive. Finally, we construct a discrete graph such that the associated
C^*-algebra is prime but not primitive.
