We associate C*-algebras to infinite directed graphs that are not necessarily locally finite. By realizing these algebras as Cuntz-Krieger algebras in the sense of Exel and Laca, we are able to give criteria for their uniqueness and simplicity, generalizing results of Kumjian, Pask, Raeburn, and Renault for locally finite directed graphs.
Fowler, N. J., Laca, M. & Raeburn, I. (2000). The C*-algebras of infinite graphs. Proceedings of the American Mathematical Society, 128 (8), 2319-2327.