Graph entropy is a concept that quantifies the amount of uncertainty or randomness in the structure of a graph. It draws on ideas from information theory and statistical mechanics to provide a measure of the complexity or diversity of a graph's configuration. There are several ways to define and calculate graph entropy, depending on the context and the specific properties one wishes to analyze.
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For a vertex law on a graph, choose and an independent set valued random variable containing almost surely. Minimize their mutual information over all such joint laws. This defines graph entropy. It differs from the entropy of a proper coloring, because the random independent set need not be a deterministic color class.