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.

翻译：克纳于1973年引入图熵概念，将其定义为字母表中并非所有字母对均可区分时自然编码问题的最小码率。后续研究表明，该熵值可表示为顶点打包多面体上最小化问题的解。本文将此概念推广至图顿，证明相应的最小化问题可为图顿熵提供上界，同时通过最大化问题形式给出下界。本文主要结果表明，对于大多数图顿而言，这两个界实际上相等，从而精确确定了所求熵值。此外，图顿熵与分数色数及分数团数之间存在紧密关联。