This set of MCQ(multiple choice questions) focuses on the **Social Networks NPTEL Week 8 Assignment Solutions**.

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

Week 1:Â *Introduction*

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

Week 3: **Strength of Weak Ties**

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

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

Week 6: **Link Analysis**

Week 7:Â **Cascading Behaviour in Networks**

Week 8:Â Link Analysis (Continued)

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

Week 10:Â **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 8 Assignment Solutions

**Q1.** Let C be the unit circle with (0,0) as its origin in the XY – plane. Then A, the point at which the vector (6,8) intersects C, is

a) (0,0)

b) (6, 8)

c) (0.6, 0.8)

d) (0.006, 0.008)

**Answer:** c) (0.6, 0.8)

**Q2.** Observe the graph shown in Figure 1, where A, B, P1, P2 and P3 are the points contained by the respective nodes. According to the principle of repeated improvement, which of the following is correct?:

a) A = P1 Ã— P2,B = P1 Ã— P3, P1 = A + B, P2 = A, P3 = B

b) A = P1 + P2,B = P1 + P3, P1 = A Ã— B, P2 = A, P3 = B

c) A = P1 + P2,B = P1 + P3, P1 = A + B, P2 = A, P3 = B

d) A = P1 + P2,B = P1 + P3, P1 = A Ã— B, P2 = 0, P3 = 0

**Answer:** c) A = P1 + P2,B = P1 + P3, P1 = A + B, P2 = A, P3 = B

**Q3.** Given a vector (3, 4) in the XY plane, what will this vector become after being pulled to the unit circle as shown in the Figure 2?

a) 4/5, 3/5

b) 4/25, 3/25

c) 3/5, 4/5

d) 3/25, 4/25

**Answer:** c) 3/5, 4/5

**Q4.** For what values of pageranks of the nodes in Figure 3 does the process converge, i.e. pageranks of the nodes do not change after this configuration?

a) Node 1: 1/5, Node 2: 1/5, Node 3: 1/5, Node 4 = 1/5, Node 5 : 1/5

b) Node 1 : 1/5, Node 2 : 1/5, Node 3 : 2/5, Node 4 : 1/10, Node 5 = 1/10

c) Node 1 : 3/10, Node 2 : 1/10, Node 3 : 1/10, Node 4 : 2/10, Node 5 : 3/10

d) Node 1 : 1/10, Node 2 : 3/10, Node 3 : 2/10, Node 4 : 1/10, Node 5 = 3/10

**Answer:** c)

**Q5.** In Hubs and Authorities algorithm, the authority update rule is defined as

a) For each page p, update auth(p) to be the sum of the hub scores of all pages that point to it.

b) For each page p, update auth(p) to be the sum of the authority scores of all pages that it points to.

c) For each page p, update auth(p) to be the sum of the hub scores of all pages that it points to.

d) For each page p, update auth(p) to be the sum of the authority scores of all pages that points to it.

**Answer:** a)

**Q6.** In the graph shown in the figure below, assume that the current page rank values of the nodes 0, 1, 2 and 3 are 0.2, 0.3, 0.4 and 0.5 respectively. What will be their pagerank values after one iteration?

a) 0.5 , 0.2, 0.3, 0.4

b) 0.6 , 0.3, 0.4, 0.5

c) 0.3, 0.4, 0.5. 0.6

d) 0.5 , 0.2, 0.4, 0.3

**Answer:** a)

**Q7.** Given two linearly independent vectors v1 and v2, which of the following is true?

a) Any other vector can be written as the linear combination of v1 and v2. i.e. z=Î±v1+Î²v2.

b) Any other vector can be written as sum of v1 and vv2. i.e. z=v1+v2.

c) Any other vector can be written as difference of v1 and v2. i.e. z=v1âˆ’v2.

d) Any other vector can be written as multiplication of v1 and v2. i.e. z=v1Ã—v2

**Answer:** a)

**Q8.** Given the graph as shown in the figure below, while calculating the pagerank using matrix multiplication method on this graph, how does the first matrix operation look like?

**Answer:** b)

**Q9.** When we add two vectors in the XY plane, where one vector has a very high magnitude as compared to the other, then the resultant vector is closer towards (in terms of direction) to

a) the bigger vector

b) the smaller vector

c) origin

d) None of the above

**Answer:** a)

**Q10.** In social networks

a) Hubs represent pointers and authorities represent resources

b) Hubs represent resources and authorities represent pointers

c) Both hubs and pointers represent resources

d) Both hubs and pointers represent pointers

**Answer:** a)

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