This set of MCQ(multiple choice questions) focuses on the **Social Networks NPTEL Week 9 Assignment Solutions**.

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**Week 0: ****Assignment answers**

Week 1: *Introduction*

Week 2: **Handling Real-world Network Datasets**

Week 3: **Strength of Weak Ties**

Week 4: **Strong and Weak Relationships (Continued) & Homophily**

Week 5: **Homophily Continued and +Ve / -Ve Relationships**

Week 6: **Link Analysis**

Week 7: **Cascading Behaviour in Networks**

Week 8: **Link Analysis (Continued)**

Week 9: Power Laws and Rich-Get-Richer Phenomena

Week 10: **Power law (contd..) and Epidemics**

Week 11: **Small World Phenomenon **

Week 12: **Pseudocore (How to go viral on web)**

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**Social Networks** NPTEL 2022 Week 9 Assignment Solutions

**Q1.** In G(1000, 0.5) random network, each edge will be placed with the probability:

a) 0.5

b) 0.9

c) 0.1

d) 0.7

**Answer:** a) 0.5

**Q2.** Which of the following correctly depicts the meaning of ‘Weight distribution of people in a city’?

a) Plot different weight values on the X axis and the fraction/percentage of people having those weights on the Y axis.

b) Plot different weight values on the X axis and the fraction/percentage of people having weights greater than those heights on the Y axis.

c) Plot different weight values on the X axis and the fraction/percentage of people having weights less than those heights on the Y axis.

d) None of the above

**Answer:** a)

**Q3.** Given a random graph on 100 nodes where each of the possible (100/2) edges is present with a probability of 0.1. Let N1 represent the number of nodes having the least degree (i.e. 0), N2 represent the number of nodes having the highest degree (i.e. 99) and N3 represent the number of nodes having the median values of degrees (i.e. 49 or 50 ). Choose the correct statement.

a) N_{1} > N_{3} and N_{2} > N_{3}

b) N_{1} < N_{3} and N_{2} < N_{3}

c) N_{1} > N_{3} and N_{2} < N_{3}

d) N_{1} < N_{3} and N_{2} > N_{3}

**Answer:** c)

**Q4.** Given set E={1,2,3,…,19,20}. We pick a value a1 uniformly at random from this set E. Next, we pick another value a2, again uniformly at random from this set EE. Similarly we pick 18 more values, a3,a4,……,a20 (a total of 20 numbers are picked). Look at the sum S=a1+a2+….+a20. Which of the following sets define the range from which the sum SS can have values from?

a) {1, 2, …, 19, 20}

b) {20, 11, …, 19, 200}

c) {1, 2, …, 9, 400}

d) {20, 11, …, 399, 400}

**Answer:** d)

**Q5.** Given set E = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. We pick a value a1 uniformly at random from this set E. Next, we pick another value a2, again uniformly at random from this set E. Similarly we pick 8 more values, a3,a4,……,a10. Look at the sum S=a1+a2+….+a10. Let p(i) be the probability that S=i, i.e., the probability that the sum of these randomly chosen 10 elements is i. Which of the following is true?

a) p(50) < p(100)

b) p(100) < p(50)

c) p(50) < p(10)

d) p(100) < p(10)

**Answer:** a)

**Q6.** Which of the following represents the correct equation for power law?

a) y = 1/x^{3}

b) y = 1/x^{4}

c) y = 1/x^{5}

d) All of the above

**Answer:** d)

**Q7.** Given a network being generated by ‘rich get richer’ phenomenon. The following Figure shows the snapshot of the network at time t. A new node ‘u’ enters the network at time t+1 and makes an edge with one of the existing nodes. The probability of ‘u’ making an edge with an existing node ‘w’ is defined as p(w). Which of the following equations is correct?

a) p(A) < p(C) < p(B)

b) p(E) < p(D) < p(B)

c) p(F ) < p(C) < p(B)

d) All of the above

**Answer:** d)

**Q8.** How does the power law degree distribution come by in real world networks?

a) By preferential attachment

b) By random linking

c) By uniform edge connection

d) No hypothesis is found

**Answer:** a)

**Q9.** In the preferential attachment, a new coming node will prefer to make the connection with the node having ________

a) fewer friends

b) More friends

c) Average number of friends

d) None of the above

**Answer:** b)

**Q10.** Given a network being generated by ‘rich get richer’ phenomenon. Figure 1 shows the snapshot of the network at time t. A new node u enters the network at time t+1 and makes an edge with one of the existing nodes. What is the probability that u will make an edge with C?

a) 1/2

b) 1/5

c) 1/3

d) 1/4

**Answer:** d)

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