Generating Infinite Random Graphs

Abstract

We define a growing model of random graphs. Given a sequence of nonnegative integers {dn} ∞ n=0 with the property that d i ≤ i, we construct a random graph on countably infinitely many vertices v 0 , v 1 . . . by the following process: vertex v i is connected to a subset of {v 0 , . . . , v i−1 } of cardinality d i chosen uniformly at random. We study the resulting probability space. In particular, we give a new characterization of random graph and we also give probabilistic methods for constructing infinite random trees.