High Quality Content by WIKIPEDIA articles! n mathematics, a random graph is a graph that is generated by some random process. The theory of random graphs lies at the intersection between graph theory and probability theory, and studies the properties of typical random graphs. A random graph is obtained by starting with a set of n vertices and adding edges between them at random. Different random graph models produce different probability distributions on graphs. Most commonly studied is the Erd?s–Renyi model, denoted G(n,p), in which every possible edge occurs independently with probability p. A closely related model, denoted G(n,M), assigns equal probability to all graphs with exactly M edges. The latter model can be viewed as a snapshot at a particular time (M) of the random graph process, which is a stochastic process that starts with n vertices and no edges and at each step adds one new edge chosen uniformly from the set of missing edges.

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