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We associate to each row-finite directed graph E a universal Cuntz-Krieger C * -algebra C * (E), and study how the distribution of loops in E affects the structure of C * (E). We prove that C * (E) is AF if and only if E has no loops. We describe an exit condition (L) on loops in E which allows us to prove an analogue of the Cuntz-Krieger uniqueness theorem and give a characterisation of when C * (E) is purely infinite. If the graph E satisfies (L) and is cofinal, then we have a dichotomy: if E has no loops, then C * (E) is AF; if E has a loop, then C * (E) is purely infinite. , The ideal structure of groupoid crossed product C * -algebras, J. Operator Theory, 25 (1991), 3-36.

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We classify the gauge-invariant ideals in the C * -algebras of infinite directed graphs, and describe the quotients as graph algebras. We then use these results to identify the gauge-invariant primitive ideals in terms of the structural properties of the graph, and describe the K-theory of the C * -algebras of arbitrary infinite graphs.