How is the clustering coefficient defined for random graphs? For example, a first definition could be calling clustering coefficient of a random graph the expected value of the clustering coefficient observed for every realization. According to this definition, how to compute the clustering coefficient for the Erdos-Renyi model? Is this a good definition?

This is a good definition. The answer can be found in the following thread: Expected global clustering coefficient for Erdős–Rényi graph

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