Question

Suppose that a team of anthropologists is studying a set of three small villages that neighbor one another. Each village has 30 people. 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 find 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. Is this network on 90 people balanced? Give a brief explanation for your answer.

Answer 1

Total no. of people=90

Total no. of people in 1 village=30

Total no. of people in other village=60

For a single person say x will have 60 enemies and only 29 friends.

Hence, it is not balanced as enemies will always win.