  We study Kazdan-Warner equations on a connected finite graph via the method
of the degree theory. Firstly, we prove that all solutions to the Kazdan-Warner
equation with nonzero prescribed function are uniformly bounded and the Brouwer
degree is well defined. Secondly, we compute the Brouwer degree case by case.
As consequences, we give new proofs of some known existence results for the
Kazdan-Warner equation on a connected finite graph.
