Rulers and slaves in a random social group

LetD(n, d) be a digraph chosen at random from a family of alld-out-regular digraphs onn points. LetK(n, p) be a simple graph onn points in which each edge appears independently with probabilityp. A relationship between the properties of extreme in-degrees ofD(n,d) and extreme degrees ofK(n, p) in the case whend = (n – 1)p = o(n) is presented. A sociological interpretation is also provided.