The model introduced here in archaeology is used in sociology to analyze relationships

Chapter 2, Problem 31

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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: aii = 0 for all i (diagonal elements of A are zero) aii = O if i and j are not friends (a) Prove that if F = AA1, then fii is the number of friends that i and j have in common. DEFINITION (b) Suppose that all friendships are not mutual. How does this affect the model?

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