2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64593We introduce a new class of C^*-algebras, which is a generalization of both graph algebras and homeomorphism C^*-algebras. This class is very large and also very tractable. We prove the so-called gauge-invariant uniqueness theorem and the Cuntz-Krieger uniqueness theorem, and compute the K-groups of our algebras.37 pages, some terminologies changed, for example, C^*-correspondences were called Hilbert C^*-bimodules and topological graphs were called continuous graphsOperator Algebras46L05, 46L55text