Rulers and slaves in a random social group

Abstract

Abstract. Let D(n, d) be a digraph chosen at random from a family of all d-out-regular digraphs on n points. Let K(n, p) be a simple graph on n points in which each edge appears independently with probability p. A relationship between the properties of extreme in-degrees of D(n, d) and extreme degrees of K (n, p)in the case when d = (n .-1)p = o(n)is presented. A sociological interpretation is also provided.

Degree sequences of random digraphs and bipartite graphs

“…Palka and Sperling showed that if we fix p such that np = w(n) log n = o(n), then any fixed number of the smallest and largest degrees are unique in G p and in the uniform G t model [37]. A similar result for the G t model is shown by Palka in [35], where t = (d, d, . .…”

In-degree sequence in a general model of a random digraph

“…We show that the indegree sequence of D(n, P) behaves similarly to the degree sequence of the classical model of a random graph (see [11]). Our results generalize those presented in [10].…”