  The entropy of a digraph is a fundamental measure which relates network
coding, information theory, and fixed points of finite dynamical systems. In
this paper, we focus on the entropy of undirected graphs. We prove that for any
integer $k$ the number of possible values of the entropy of an undirected graph
up to $k$ is finite. We also determine all the possible values for the entropy
of an undirected graph up to the value of four.
