  K\"orner introduced the notion of graph entropy in 1973 as the minimal code
rate of a natural coding problem where not all pairs of letters can be
distinguished in the alphabet. Later it turned out that it can be expressed as
the solution of a minimization problem over the so-called vertex-packing
polytope.
  In this paper we generalize this notion to graphons. We show that the
analogous minimization problem provides an upper bound for graphon entropy. We
also give a lower bound in the shape of a maximization problem. The main result
of the paper is that for most graphons these two bounds actually coincide and
hence precisely determine the entropy in question. Furthermore, graphon entropy
has a nice connection to the fractional chromatic number and the fractional
clique number.
