Social Networks | Week 8

Social Networks Week 8 Assignment 8 Answers

Course Link: Social Networks | Week 8

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

Q2. Pick out all the properties of a markov matrix
largest eigen value is 1
smallest eigen value is 1
sum of any column is 1
sum of any column is 0

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

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 update

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

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)

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

Q8. Pick out the matrix that represents the given graph H to view page rank as a matrix multiplication process:
⎡⎣⎢⎢⎢⎢0110100001/201/21/21/200⎤⎦⎥⎥⎥⎥
⎡⎣⎢⎢⎢⎢0010100001/211/21/21/200⎤⎦⎥⎥⎥⎥
⎡⎣⎢⎢⎢⎢0010100011/201/21/21/200⎤⎦⎥⎥⎥⎥
⎡⎣⎢⎢⎢⎢0010100001/201/21/21/200⎤⎦⎥⎥⎥⎥

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

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