# Question

Consider a graph having n vertices labeled 1, 2, . . . , n, and suppose that, between each of the

pairs of distinct vertices, an edge is independently present with probability p. The degree of vertex i, designated as Di, is the number of edges that have vertex i as one of their vertices.

(a) What is the distribution of Di?

(b) Find ρ(Di, Dj), the correlation between Di and Dj.

pairs of distinct vertices, an edge is independently present with probability p. The degree of vertex i, designated as Di, is the number of edges that have vertex i as one of their vertices.

(a) What is the distribution of Di?

(b) Find ρ(Di, Dj), the correlation between Di and Dj.

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