Erdos-Renyi random graphs aren't mentioned probably because they hold almost no relevance to social graphs and networks, like the ones being addressed by Metcal

Erdos-Renyi random graphs aren't mentioned probably because they hold almost no relevance to social graphs and networks, like the ones being addressed by Metcalfe's and Zipf's law. Erdos-Renyi random graphs have a Gaussian degree distribution (or maybe Poissonian degree distribution) [1] which effectively makes the number of edges a proportion of the number of vertices with a narrow band of variation as a result of the finite variance. Social networks tend to have some type of power law or "long tailness" to them, giving them unbounded variance of degree and often giving them unbounded mean degree [2] [3]. Another way to say this is Erdos-Renyi random graphs are not long tailed, power law degree distributed or scale free, which Metcalf's law and Zipf distributions address in one form or another. [1] https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93R%C3%A9nyi_model#Properties_of_G(n,_p) https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93R%C3%A9nyi_... [2] https://en.wikipedia.org/wiki/Long_tail https://en.wikipedia.org/wiki/Long_tail [3] https://en.wikipedia.org/wiki/Stable_distribution https://en.wikipedia.org/wiki/Stable_distribution