## NPTEL Social Networks Week 8 Assignment Answers 2024

1. In an academic research network, where researchers cite other researchers’ work and are cited by others, which of the following is correct?

- Researchers who cite other researchers are represented by hubs, and researchers whose work is cited are represented by authorities
- Researchers who are cited by others are represented by hubs, and researchers who cite others are represented by authorities
- Both researchers who cite others and researchers who are cited act as hubs
- Both researchers who are cited and researchers who cite others act as authorities

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2. In the graph G shown in the following figure, assume that the current pagerank values of A, B and C are 0.5, 0.4 and 0.1 respectively. What will be their pagerank values after one iteration?

- A: 0.2,B: 0.4,C: 0.4
- A: 0.2,B: 0.1,C: 0.7
- A: 0.1,B: 0.2,C: 0.7
- A: 0.7,B: 0.2,C: 0.1

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3. Given a network P with 8 nodes with an initial page rank value of 1/8 each. What is the page rank value of node B at the end of 2 iterations?

- 1/8
- 1/4
- 1/32
- 1/64

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4. Assume we perform a sequence of k hub-authority updates. Each update works as follows: First apply the Authority Update Rule to the current set of scores.Then apply the Hub Update Rule to the resulting set of scores. At the end, the hub and authority scores may involve numbers that are very large. Select all that is TRUE.

- We care only about their relative sizes
- we can normalise them
- we can simply reduce each value by a fixed value in every iteration
- we care only about their absolute values

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5. Assume the hub and authority score for each node in the given graph J as 1. What is the hub and authority score of node 3 in the given graph J in iteration k=1?

- a(1)= 1,h(1)= 2
- a(1)= 2,h(1)= 1
- a(1)= 3,h(1)= 2
- a(1)= 2,h(1)= 3

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6. Consider the following bipartite graph, which of the following is/are correct for repeated improvement?

- B = P1 + P3
- C = P3 + P4
- P2 = A + B
- P3 = B

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7. Which of the following is TRUE for a Markov Matrix?

Statement I – The sum of elements in every column is 1.

Statement II – Highest eigenvalue of a Markov matrix is 1.

- I only
- II only
- Both
- None

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8. For the given network H, what are the values after say 10 iterations of Page rank updates for the initial value of 1/3 for every node in the network?

- 0.17,0.50,0.33
- 0.33,0.33,0.33
- 0.50,0.17,0.33
- 0.22,0.44,0.33

Answer :-

9. Which of the following best describes the process for updating the authority scores of web pages in the Hubs and Authorities Algorithm?

- Update the authority score of a page p by summing the hub scores of all pages with hyperlinks pointing to p.
- Update the authority score of a page p by summing the authority scores of all pages to which p has outbound hyperlinks.
- Update the authority score of a page p by summing the hub scores of all pages to which p has outbound hyperlinks.
- Update the authority score of a page p by summing the authority scores of all pages that p points to.

Answer :-

10. Let C be a unit circle with center at (0,0) in the XY-plane. Then H, the point at which the vector(4,3) intersects C is

- (0,0)
- (3,4)
- (0.6,0.8)
- (0.8,0.6)

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