# Social Networks | Week 8

**Session: JULY-DEC 2023**

**Course Name: Social Networks**

**Course Link: Click Here**

**These are Nptel Social Networks Week 8 Assignment 8 Answers**

**Q1. Consider a network of recommenders and resources, where higher rating represents a good one. What are the factors that contribute to a good rating for a node P?I. Good nodes pointing to PII. P pointing to good nodes**

I only

II only

Both I and II

None

**Answer: Both I and II**

**Q2. Pick out all the properties of a markov matrix**

largest eigen value is 1

smallest eigen value is 1

sum of any coumn is 1

sum of any column is 0

**Answer: A, C**

**Q3. Identify whether the statements are True.Statement I – When a matrix is applied on its eigenvectors, the direction of the eigenvector only changesStatement II – Eigenvectors are linearly independent of each other**

I only

II only

II only

None

**Answer: II only**

**These are Nptel Social Networks Week 8 Assignment 8 Answers**

**Q4. Consider a directed network having nodes A,B,C and edges (B,A), (A,C), (C,B), (B,C). The current pagerank values of and 0.2, 0.4 and 0.4 respectively. What will be their pagerank after one iteration? Apply the basic page update rule ignoring evaporation/teleportation.**

A:0.2,B:0.2,C:0.4

A:0.4,B:0.2,C:0.2

A:0.4,B:0.2,C:0.4

A:0.2,B:0.4,C:0.4

**Answer: A:0.2,B:0.4,C:0.4**

**Q5. According to Google Page rank, a web page is important if**

a lot of other pages refer to this page

the page recommends a lot of other pages

important pages refer to this page

unimportant pages refer to this page

**Answer: important pages refer to this page**

**Q6. What will be the resultant vector when we apply the matrix A on the vector (3, 5)?A=[5142]**

(13, 35)

(35, 13)

(16, 22)

(22, 16)

**Answer: (35, 13)**

**These are Nptel Social Networks Week 8 Assignment 8 Answers**

**Q7. If a Markov matrix X whose eigenvectors and eigenvalues are υ1,υ2 and λ1,λ2 respectively is applied on a vector V repeatedly k times, which of the following is true assuming we that we normalise the resultant vector after each iteration and λ1 is the greater eigenvalue and k is very large?**

AkV=υ1

AkV=υ2

AkV=υ1+υ2

AkV=υ1−υ2

**Answer: A^kV=υ1**

**Q8. Pick out the matrix that represents the given graph H to view page rank as a matrix multiplication process:**

⎡⎣⎢⎢⎢⎢0 1 1 0 1 0 0 0 0 1/2 0 1/2 1/2 1/2 0 0⎤⎦⎥⎥⎥⎥

⎡⎣⎢⎢⎢⎢0 0 1 0 1 0 0 0 0 1/2 1 1/2 1/2 1/2 0 0⎤⎦⎥⎥⎥⎥

⎡⎣⎢⎢⎢⎢0 0 1 0 1 0 0 0 1 1/2 0 1/2 1/2 1/2 0 0⎤⎦⎥⎥⎥⎥

⎡⎣⎢⎢⎢⎢0 0 1 0 1 0 0 0 0 1/2 0 1/2 1/2 1/2 0 0⎤⎦⎥⎥⎥⎥

**Answer: d. ⎡⎣⎢⎢⎢⎢0 0 1 0 1 0 0 0 0 1/2 0 1/2 1/2 1/2 0 0⎤⎦⎥⎥⎥⎥**

**These are Nptel Social Networks Week 8 Assignment 8 Answers**

**Q9. Which of the following are TRUE for the Hubs and Authorities algorithm?Statement I – The Authority update rule states that for each page p, update auth(p) is the sum of the authority scores of all pages that point to it.Statement II – The Hub update rule states that for each page p, update hub(p) is the sum of the hub scores of all pages that it points to.**

I only

II only

Both

None

**Answer: None**

**These are Nptel Social Networks Week 8 Assignment 8 Answers**

**Q10. What is the score value of authority(a) and hub(h) respectively for node 4 in the following figure after applying 1-step hub-authority computation (i.e. when k is 1)?Assume initial hub and authority of each node as 1.**

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

a(1)=0, h(1)=3

a(1)=3, h(1)=0

a(1)=0, h(1)=0

**Answer: a(1)=3, h(1)=0**

**These are Nptel Social Networks Week 8 Assignment 8 Answers**

More Weeks of Social Networks: Click here

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**Session: JAN-APR 2023**

**Course Name: Social Networks**

**Course Link: Click Here**

**These are Nptel Social Networks Week 8 Assignment 8 Answers**

**These are Nptel Social Networks Week 8 Assignment 8 Answers****Q1. Consider the following graph G. What is the formula used to apply the principle of repeated improvement before normalisation to obtain convergence?**

a. A = P1 + P2 + P4, B = P1 + P3, C = P2 + P4, P1 = A + B, P2 = A + C, P3 = B, P4 = A + C

b. A = P1 + P3 + P4, B = P1 + P3, C = P2 + P4, P1 = A + B, P2 = A + C, P3 = B, P4 = A + C

c. A = P1 + P2 + P4, B = P1 + P3, C = P2 + P4, P1 = A + B, P2 = A + C, P3 = B, P4 = A + B

d. A = P1 + P2 + P3, B = P1 + P3, C = P2 + P4, P1 = A + B, P2 = A + C, P3 = B, P4 = A + C

**Answer: a. A = P1 + P2 + P4, B = P1 + P3, C = P2 + P4, P1 = A + B, P2 = A + C, P3 = B, P4 = A + C**

**Q2. For the given network H, what will happen after say 10 iterations of Page rank updates for the initial value of 1/3 for every node in the network**

a. The value at A steadily increases

b. The value at C steadily decreases

c. The value at C steadily increases

d. The value at B steadily increases

**Answer: c. The value at C steadily increases**

**These are Nptel Social Networks Week 8 Assignment 8 Answers**

**Q3. Consider a Graph H shown in figure 2. Which of the following is True for this graph?**

a. Doesnot converge

b. Converges with all points in node C

c. Converges zero points in node C

d. Converges with maximum points in A and B

**Answer: b. Converges with all points in node C**

**These are Nptel Social Networks Week 8 Assignment 8 Answers**

**Q4. Pick out the matrix that represents the given graph J to view page rank as a matrix multiplication process:**

a. ⎡⎣⎢0011/201/2010⎤⎦⎥

b. ⎡⎣⎢001101010⎤⎦⎥

c. ⎡⎣⎢01/211/201/2010⎤⎦⎥

d. ⎡⎣⎢01/21/21/201/2010⎤⎦⎥

**Answer: d. ⎡⎣⎢01/21/21/201/2010⎤⎦⎥**

**Given a matrix M, M=[4352]and a vector V=[23]Apply M on V and normalise it to obtain the resultant vector, R=[ab]Note: Precision level of at least four decimal places to be considered for computation**

**Q5. Enter the value of a ______________.**

**Answer: 0.88,0.89**

**Q6. Enter the value of b ______________.**

**Answer: 0.455,0.465**

**These are Nptel Social Networks Week 8 Assignment 8 Answers**

**Q7. Which of the following are TRUE for the Hubs and Authorities algorithm?Statement I – The Authority update rule states that for each page p, update auth(p) is the sum of the hubscores of all pages that point to it.Statement II – The Hub update rule states that for each page p, update hub(p) is the sum of the authorityscores of all pages that it points to.**

a. I only

b. II only

c. Both

d. None

**Answer: c. Both**

**Assume the shown pageranks for the given nodes at some point of time. **

**Q8. Find the page rank score of web pages B in the next iteration:**

**Answer: 6.5**

**These are Nptel Social Networks Week 8 Assignment 8 Answers**

**Q9. Find the page rank score of web pages D in the next iteration:**

**Answer: 5.5**

**Q10. What is the score value of authority(a) and hub(h) respectively for node 5 in the following figure after applying 1-step hub-authority computation (i.e. when k is 1)?Assume initial hub and authority of each node as 1.**

a. a(1)=3, h(1)=3

b. a(1)=3, h(1)=0

c. a(1)=0, h(1)=3

d. a(1)=0, h(1)=0

**Answer: c. a(1)=0, h(1)=3**

**These are Nptel Social Networks Week 8 Assignment 8 Answers**

**Q11. Two vectors V1 and V2 are added in the XY plane. Given that V1 is of a very high magnitude when compared to V2, then the resultant vector is**

a. same as V1

b. independent of V2

c. closer to the direction of V1

d. closer to the direction of V2

**Answer: c. closer to the direction of V1**

**Q12. Which of the following is TRUE for a Markov Matrix?Statement I – The sum of elements in every column is same.Statement II – Highest eigenvalue of a Markov matrix is 1.**

a. I only

b. II only

c. Both

d. None

**Answer: b. II only**

**These are Nptel Social Networks Week 8 Assignment 8 Answers**

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