If instead we start with an infinite set of vertices, and again let every possible edge occur independently with probability 0 < p < 1, then we get an object G called an infinite random graph. Except in the trivial cases when p is 0 or 1, such a G almost surely has the following property:

Given any n + m elements , there is a vertex c in V that is adjacent to each of and is not adjacent to any of .

It turns out that if the vertex set is countable

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