This question is from \" Networks, Crowds, and Markets: Reasoning about a Highly

Question

This question is from " Networks, Crowds, and Markets: Reasoning about a Highly Connected World" textbook in chapter 5 Suppose that a team of anthropologists is studying a set of three small villages that neighbor one another. Each village has 30 people, consisting of 2-3 extended families. 5.6. Everyone in each village knows all the people in their own village, as well as the people in the other villages. When the anthropologists build the social network on the people in all three villages taken together, they and that each person is friends with all the other people in their own village, and enemies with everyone in the two other villages. This gives them a network on 90 people (i.e., 30 in each village), with positive and negative signs on its edges. According to the definition in this chapter, is this network on 90 people balanced? Give a brief explanation for your answer.

Explanation / Answer

SOLUTION:- Let Village 1 = X, Village 2 = Y, Village 3 = Z

As given in this question that each person is friends with all the other people in their own village, and enemies with everyone in the two other villages that means X, Y, and Z are mutual enemies with negative sign on all of its edges so In this network on 90 people is not balanced. As per the concept of struture balance in a 3 node network there should be a positive sign on its all 3 edges or should atleast 1 positive sign on any of its edge then that given network will be called balanced but here is negative sign exists on all edges so This network on 90 people is not balanced.

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