## NPTEL Social Networks Week 7 Assignment Answers 2024

1. Assume that actions X and Y yield every player a payoff of 5 and 10 respectively. Further assume that there are two friends, Alex and Blake. Alex decides to adopt action X while Blake decides to adopt action Y. What are the payoffs that they get?

- 5,10
- 5,0
- 10,5
- 0,10

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2. In a company, a new software is being introduced. Employees will only adopt the software if at least a fraction q of their colleagues have started using it. If a few tightly-knit departments of employees work closely with each other, what could prevent the software from being adopted company-wide?

- The department has fewer than q of the employees
- The department has fewer than 1 – q of the employees
- The department has more than q of the employees
- The department has more than 1 – q of the employees

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3. In the context of viral marketing, a company aims to promote a new product by targeting key individuals in a social network. These individuals are selected based on their ability to influence others within the network. Given that the network has varying degrees of connectivity among its members, which of the following strategies is most effective for maximizing the spread of the product?

- Target individuals with the highest number of direct connections, regardless of their influence on others
- Target individuals who are central to the network, as they act as bridges between different groups
- Target the most isolated individuals, as they are less likely to have been influenced by others
- Target individuals who are closely connected within a small, dense cluster, as they can influence others within their immediate group

Answer :-

4. Given a node X having 10 friends/neighbors. 3 of its neighbors have decided to adopt the behavior/action A having a payoff of 10 while 7 of its friends have adopted the action B yielding a payoff of 4. What is the payoff that X gets from its friends who have adopted action A?

- 30
- 70
- 12
- 40

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5. For the node X mentioned in question 4, What is the payoff that X gets from its friends who have adopted B?

- 30
- 40
- 28
- 38

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6. For node X mentioned in question 4, What is the final action/behavior that X would adopt?

- A
- B
- neither A nor B
- cannot say

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7. For the given figure, what is the density of community formed by nodes A, B, C and D?

- 0
- 1
- 2
- 3

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8. Given the network below, if the value above the node is its threshold value to join the protest, is the protest likely to happen?

- Yes
- No
- Cannot say

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9. Given a network as shown in the following Figure, assume that initially, every node in this network has adopted behavior B. Next, a new behavior A is introduced in the network and nodes 1 and 3 are the initial adopters of this behavior A, i.e., nodes 1 and 3 now have adopted behavior A and the rest of the nodes have adopted behavior B. The payoff associated with A is a = 3 and the payoff associated with B is b = 2. After the introduction of this new behavior A in the network, all the nodes will start weighing their options and might change their behavior. This leads to a cascade in the network. When the cascade ends, identify the nodes that will adopt the behavior A.

- 1,3,2
- 1,3,2,4
- 1,3,2,7
- 1,3,2,7,5

Answer :-

10. Let v be a node in a graph. Suppose that a fraction α of the neighbors of v has adopted behavior X, and a fraction 1 − α has adopted behavior Y. In other words, if v has k neighbors, then αk neighbors adopt X, and (1−α)k neighbors adopt Y. Behavior X yields a payoff of x, and behavior Y yields a payoff of y. Behavior X is a more advantageous choice for v if:

- α≥x/y
- α≥y/x
- α≥x/(x+y)
- α≥y/(x+y)

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