Consider a graph having $n=8$

vertices labeled $1,2,...,8$ . Suppose that each edge is independently present with probability p. The degree of vertex i, designated as ${D}_{i}$ , is the number of edges that have vertex i as one of its vertices. Find $Corr({D}_{i},{D}_{j})$ , the correlation between ${D}_{i}$ and ${D}_{j}$ .

vertices labeled $1,2,...,8$ . Suppose that each edge is independently present with probability p. The degree of vertex i, designated as ${D}_{i}$ , is the number of edges that have vertex i as one of its vertices. Find $Corr({D}_{i},{D}_{j})$ , the correlation between ${D}_{i}$ and ${D}_{j}$ .