Question: =+25. Consider a random graph with n nodes. Between every pair of nodes, we independently introduce an edge with probability p. A trio of nodes

=+25. Consider a random graph with n nodes. Between every pair of nodes, we independently introduce an edge with probability p. A trio of nodes forms a triangle if each of its three pairs is connected by an edge. If N counts the number of triangles, then demonstrate that E(N) = n 3

p3 and Var(N) = n 3

p3(1 − p3) + n 3

3(n − 3)(p5 − p6).

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