# NPTEL Social Networks Assignment 7 Answers 2022

Are you looking for the Answers to NPTEL Social Networks Assignment 7? This article will help you with the answer to the National Programme on Technology Enhanced Learning (NPTEL) Course “NPTEL Social Networks Assignment 7

## What is Social Networks?

The world has become highly interconnected and hence more complex than ever before. We are surrounded by a multitude of networks in our daily life, for example, friendship networks, online social networks, world wide web, road networks etc. All these networks are today available online in the form of graphs which hold a whole lot of hidden information. They encompass surprising secrets which have been time and again revealed with the help of tools like graph theory, sociology, game theory, etc.

## CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of the average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF THE AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Below you can find the answers for the NPTEL Social Networks Assignment 7

## NPTEL Social Networks Assignment 7 Answers:-

Q1. Assume that the actions A and B yield every player a payoff of a and b. Further assume that there are two friends Ram and Shyam; Ram decides to adopt action A while Shyam decides to adopt action B. What are the payoffs that they get?

Q2. Consider a set of initial adopters of behavior A, with a threshold of q for nodes in the remaining network to adopt behavior A. Given the following two statements,
Statement 1: If the remaining network contains a cluster of density greater than 1−q, then the set of initial adopters will not cause a complete cascade.
Statement 2: Whenever a set of initial adopters does not cause a complete cascade with threshold q, the remaining network must contain a cluster of density greater than 1−q.
Choose the correct option from the following.

Q3. Consider two actions A and B. The payoff associated with the action A is 30 while the payoff associated with action B is 10. In such a case, what is the threshold fraction of neighbors that should have adopted A, in order for a node to adopt the action A?

Q4. Given a node X having 8 friends/neighbors. 3 of its neighbors have decided to adopt the behavior/action A having a payoff of 11. 5 of its friends have adopted the action B yielding a payoff of 6. What is the payoff X gets from its friends who have adopted B?

Q5. In the network shown in Figure 2, what is the density of the cluster comprised by the set of nodes {1, 2, 3, 4}?

Q6. Given a network as shown in Figure 3. Assume that initially every node in this network has adopted behavior B. Next, a new behavior A is introduced in the network and the nodes v and w are the initial adopters of this behavior A, i.e., nodes v and w now have adopted behavior A and 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. After two iterations, which nodes would have adopted the behavior A?

Q7. Let v be a node in a graph. Suppose that a p fraction of v’s neighbors have behavior A, and a (1−p) fraction have behavior B; that is, if v has d neighbors, then pd adopt A and (1−p)d adopt B, as shown in Figure 5. Behavior A has a payoff of a and behavior B has a payoff of b. Then A is a better choice for v if

Q8. Given a network as shown in Figure 6. Assume that initially every node in this network has adopted behavior B. Next, a new behavior A is introduced in the network and the nodes 1 and 3 are the initial adopters of this behavior A, i.e., nodes 1 and 3 now has adopted behavior A and rest of the nodes have adopted behavior B. The payoff associated with A is a=3 and the payoff associated with B is b=1. 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, which all are the nodes who have adopted the behavior A.

Q9. Consider a group of 10 bachelors, 5 live on the first floor of the apartment and 5 live on the second floor. Suppose that each person in this group has two friends on their own floor, and one friend on the other floor. Now, a new restaurant opens, and five persons all living on the first floor each begin eating there on the first day. This action will eventually be adopted by

Q10. Consider the following network with green nodes following the action A and red nodes following the action B at Time t = 1 (Figure 7).
The payoff for action A is 6 and for B it is 5. Each one in this network changes his/her action based on his/her friends actions. What will happen after one complete iteration.