In real world networks, we have no further information about the structure of the networks. For example, in the Facebook network, we assume each one has some known particular probabilities to influence his friends. But how can we know the probability that I influence some guy who is randomly selected in the network?
If the network is like a chain, or like a complete graph and all the probabilities are equal, it seems easy. However, in a real world network, it is usually not the case.
I mean, how can classical random graph theory be applied to real world networks? Maybe I have fallen into a trap. I am not sure if such question is legal to ask here. But I am very interested about how to deal with the gap between theoretical things with real world things.
One application of random graph theory is to serve as a "null model". Suppose you have a real-world network that has value $y$ of property $X$, for example clustering. How do you know whether $y$ is a high value? In this sense, random graph theory can help, since it can tell you how much higher it is than in a random graph (for example using the configuration model). Now you know that your value $y$ is higher or lower than expected in a completely random network.
But you are right, most classical random graph models do not resemble real-world networks. More difficult random graph models have been proposed to include more of the properties of real world networks so that they can model real-world networks more accurately.