Eight villages for Exercises 2 and 3. In this problem, we consider a network whe

Question

Eight villages for Exercises 2 and 3. In this problem, we consider a network where relationships can be positive or negative, but riot all pairs of people know each other. We say that such a network with missing edges is balanced if there is a way to add positive or negative edges between pairs of nodes not yet connected without changing the existing edges to make the network balanced (section 5.5A in the textbook). Consider again the eight villages along the river Figure 1. Now assume that the people in these villages are friends with everyone in their own village, are enemies of the people in the neighboring villages, but don't know the people in villages further away. For example, people in village 4 are friends with others in their own village, enemies of people in villages 3 and 5, but don't know people in villages 1, 2 and 6, 7, 8. Is the resulting network balanced? Provide an explanation for your answer.

Explanation / Answer

Structural Balance Property: For every set of three nodes, if we consider the three edges connecting them, either all three of these edges are labeled +, or else exactly one of them is labeled +.

Here in this question, people are friends with everyone in their own village, are enemies of the people in the neighboring villages, but don't know the people in villages further away. Hence, we have a network of all (-)ve edges between all the eight villages, thereby making them Unbalanced(Due to lack of positive edges).

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