We develop notions of a representation of a topological graph E and of a covariantrepresentation of a topological graph E which do not require the machinery ofC*-correspondences and Cuntz-Pimsner algebras. We show that the C*-algebragenerated by a universal representation of E is isomorphic to the Toeplitz algebra ofKatsura's topological-graph bimodule, and that the C*-algebra generated by a universalcovariant representation of E is isomorphic to Katsura's topological graphC*-algebra. We exhibit our results by constructing the isomorphism between theC*-algebra of a row-finite directed graph E with no sources and the C*-algebra ofthe topological graph arising from the shift map acting on the infinite-path spaceE∞.
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