C*-algebras of infinite graphs and Cuntz-Krieger algebras

The Cuntz-Krieger algebra O(B) is defined for an arbitrary, possibly infinite and infinite valued, matrix B. A graph C*-algebra G* (E) is introduced for an arbitrary directed graph E, and is shown to coincide with a previously defined graph algebra C* (E) if each source of E emits only finitely many edges. Each graph algebra G* (E) is isomorphic to the Cuntz-Krieger algebra O(B) where B is the vertex matrix of E.