Social Networks | Week 7

Session: JULY-DEC 2023

Course Name: Social Networks

Course Link: Click Here

These are Nptel Social Networks Week 7 Assignment 7 Answers

Q1. A cascade cannot be complete in a network with threshold of adoption = q, if there exist a cluster with density
lesser than q
greater tan q
lesser than (1 – q)
greater than (1 – q)

Answer: greater than (1 – q)

Q2. Let ‘x’ be a node in a graph. Suppose that a ‘p’ fraction of the neighbors of ‘x’ have behavior A, and a (1 – p) fraction have behavior B; that is, if ‘x’ has ‘d’ neighbors, then pd adopt A and (1- p)d adopt B, as shown in the following Figure. Behavior A has a payoff of ‘a’ and behavior B has a payoff of ‘b’. Then A is a better choice for ‘x’ if
p ≥ a/b
p ≥ b/a
p ≥ a/(a + b)
p ≥ b/(a + b)

Answer: p ≥ b/(a + b)

Q3. Find the cluster density of the blue color nodes shown in the given figure 14.
1/2
2/3
3/4
3/5

Answer: 3/5

These are Nptel Social Networks Week 7 Assignment 7 Answers

Q4. Which of the following are valid factors for influence diffusion?
Payoff
Key people
Both Payoff and key people
Neither Payoff nor key people

Answer: Both Payoff and key people

Q5. Consider the basic coordination based game theoretical model for cascading behavior. The payoffs associated with behaviours ‘A’ and ‘B’ are a and b respectively. Consider two friends x and y adopting behaviours ‘A’ and ‘B’ respectively. Assuming that x and y have no other friends than each other, the total payoff which they receive is
ab
a + b
a/b
b/(a + b)

Answer: a + b

Q6. 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 the 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, which all are the nodes who have adopted the behavior A.
1, 3, 2
1, 3, 2, 4
1, 3, 2, 4, 5
1, 3

See also Social Networks | Week 2

Answer: 1, 3, 2, 4

These are Nptel Social Networks Week 7 Assignment 7 Answers

Q7. Let us consider a model for collective action shown in Figure 16, where the intrinsic threshold is given for every node. Which of the following statements is INCORRECT for this case?
u will go for a protest as it has two neighbors and its threshold is two
v will not go for a protest because w has a threshold of 4 and there are only two other nodes in the network
w will not go for a protest because its threshold is 4 and there are only two neighbors
all three nodes will go for a protest as the average threshold is 3 and there are three nodes in the network

Answer: A, D

Q8. Given a node X having 10 friends/neighbors. 3 of its neighbors have decided to adopt the behavior/action A having a payoff of 12 while 7 of its friends have adopted the action B yielding a payoff of 9. What is (i) the payoff that X gets from its friends who have adopted the action A, (ii) the payoff that X gets from its friends who have adopted B, (iii) The final action/behavior adopted by X?
(i) 36 ,(ii) 63, (iii) B
(i) 63 ,(ii) 36, (iii) B
(i) 36 ,(ii) 63, (iii) A
(i) 63 ,(ii) 36, (iii) A

Answer: (i) 36 ,(ii) 63, (iii) B

Q9. Consider the social network in the Figure 17, and again let’s suppose that in the A-B coordination game. Initially, all nodes have adopted B. There are two initial adopters node 7 and 8 for A. we have a payoff of a = 3 and b = 2, what is the threshold for any node to switch from B to A?
2/3
3/2
2/5
3/5

Answer: 2/5

These are Nptel Social Networks Week 7 Assignment 7 Answers

Q10. For the A-B coordination Game mentioned in Question 9, What are the nodes that have adopted action A after the next three steps?
nodes 5 to 10
nodes 4 to 10
nodes 4 to 17
all nodes 1 to 17

These are Nptel Social Networks Week 7 Assignment 7 Answers

Q1. If the payoff of playing a game and working out in the Gym is given as 0.6 and 0.4 respectively. Four of your friends decides to play and five of them decide to work out. Which one should you pick?
a. Playing a Game
b. Work out in the Gym
c. Data insufficient to decide
d. None

Answer: a. Playing a Game

Q2. Which of the following technique helps to identify the important node in the network so that the idea spreads to the entire network very fast?
a. Community detection
b. Page ranking
c. Viral marketing
d. Embeddedness

Answer: c. Viral marketing

These are Nptel Social Networks Week 7 Assignment 7 Answers

Q3. Consider a network with adoption threshold ‘q’. A cascade cannot be complete in this network if there exists a cluster of density
a. less than q
b. less than 1-q
c. greater than q
d. greater than 1-q

Answer: b. less than 1-q

These are Nptel Social Networks Week 7 Assignment 7 Answers

Q4. Find the density of Community c1, c2 and c3 for the following network.

a. 5/6, 7/10, 8/10
b. 5/30, 7/30, 8/30
c. 4/6, 6/10, 7/10
d. 4/30, 7/30, 8/30

Answer: a. 5/6, 7/10, 8/10

These are Nptel Social Networks Week 7 Assignment 7 Answers

Q5. Consider the graph G in Figure 1, which one of the communities is difficult for an idea to be injected?
a. c1
b. c2
c. c3
d. None

Answer: a. c1

These are Nptel Social Networks Week 7 Assignment 7 Answers

Q6. Any cascade on a complete network with only one seed node
a. will always be complete
b. will always be incomplete
c. is difficult to occur
d. Can’t say – insufficient information

Answer: d. Can’t say – insufficient information

These are Nptel Social Networks Week 7 Assignment 7 Answers

Q7. What is the cluster density of the each of the four node cluster?

See also Social Networks | Week 12

a. 1/3
b. 2/3
c. 3/4
d. 4/3

Answer: b. 2/3

These are Nptel Social Networks Week 7 Assignment 7 Answers

Q8. Consider the network given in the following figure. Initially all the nodes in the network adopt an idea Y. Nodes A nd B adopt a new idea X in the network. The payoff for X is 4 and Y is 1. This leads to a cascade in the network. What are all the nodes that have adopted the behavior A when the cascade ends?

a. A, B, C
b. A, B, C, D
c. A, B, C, D, E
d. A, B, C, D, E, F
e. A, B, C, D, E, F, G, H, I, J

Answer: b. A, B, C, D

These are Nptel Social Networks Week 7 Assignment 7 Answers

Q9. Consider a network where all of its nodes have adopted an idea A. Which of the following efforts can be a valid attempt to create a complete cascade of a new idea B in such a network. Select all that is applicable.
a. Increase the payoff for the new idea
b. Identify key people in the network to inject the idea
c. Increase the payoff for idea A
d. Identify the cluster with density q

Answer: a, b

These are Nptel Social Networks Week 7 Assignment 7 Answers

Q10. Given the network K, assume a new idea has been adopted by the nodes, 0, 1, 2, 3, 4, and 5. How do you ensure that the new idea diffuses into the cluster marked by red dotted lines?

a. by diffusing it to the nodes 6 and 12
b. by identifying the correct set of nodes from outside the cluster.
c. Both
d. Cascade is incomplete and it cannot enter the cluster

Answer: d. Cascade is incomplete and it cannot enter the cluster

These are Nptel Social Networks Week 7 Assignment 7 Answers

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