A random graph is obtained by starting with a set of "n" isolated vertices and adding successive edges between them at random. The aim of the study in this field is to determine at what stage a particular property of the graph is likely to arise. Different random graph models produce different probability distributions on graphs. Most commonly studied is the one proposed by Edgar Gilbert, denoted "G"("n","p"), in which every possible edge occurs independently with probability 0 < "p" < 1. The probability of obtaining "any one particular" random graph with "m" edges is formula_1 with the notation formula_2.