  We define an ultragraph, which is a generalization of a directed graph, and
describe how to associate a C*-algebra to it. We show that the class of
ultragraph algebras contains the C*-algebras of graphs as well as the Exel-Laca
algebras. We also show that many of the techniques used for graph algebras can
be applied to ultragraph algebras and that the ultragraph provides a useful
tool for analyzing Exel-Laca algebras. Our results include versions of the
Cuntz-Krieger Uniqueness Theorem and the Gauge-Invariant Uniqueness Theorem for
ultragraph algebras.
