On the evolution of random graphs. II. (English) Zbl 0106.12006

Erdős, Pál; Rényi, Alfréd

Bull. Inst. Int. Stat. 38, No. 4, 343-347 (1961).

Let \(E_{n,N}\) denote the set of all linear graphs having \(n\) given labelled vertices and \(N\) edges. A random graph \(\Gamma_{n,N}\) is defined as an element of \(E_{n,N}\) chosen at random, so that each of the elements of \(E_{n,N}\) have the same probability to be chosen. The authors describe the process of evolution of the random graph \(\Gamma_{n,N}\) for \(n,N \to \infty\) and such that \(N=N(n)\) is a given function of \(n\).

Reviewer: G.Mihoc

MSC:

05C80

Random graphs (graph-theoretic aspects)

Keywords:

probability theory