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 P
II. 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 changes
Statement 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
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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
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 hub
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 authority
scores 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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