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

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

See also Social Networks | Week 5

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