The model introduced here in archaeology is used in sociology to analyze relationships within a group of people. For example, consider the relationship of ?friendship? within a group. Assume that all friendships are mutual. Label the people 1,?, n and define a square matrix A as follows: aij = 0 for all i (diagonal elements of A are zero)

(a) Prove that if F = AAt then fij is the number of friends that i and j have in common.

(b) Suppose that all friendships are not mutual. How does this affect the mode

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aij f1 lo ifi and j are friends if i and j are not friends aij f1 lo ifi and j are friends if i and j are not friends