## NPTEL Social Network Analysis Week 8 Assignment Answers 2024

1. In a k-core of a graph, what is true about the vertices?

- Every vertex has exactly k edges.
- Every vertex has at least k edges
- Every vertex has at most k edges

Answer :-For Answers Click Here

2. In the SIR model, a recovered node can be infected again.

- True
- False

Answer :-For Answers Click Here

**For Question 3 and 4 –**

Given the graph G1, the first node is a hard-wired adopter of A, while all others have adopted B. The payoffs for adopting A and B are a and b, respectively. Further, the cost of adopting AB (irrespective of neighborhood) is c. Between two interacting nodes, we consider the following scenarios of payoff as shown in table T1. Using the interaction system on 1, determine the strategy adopted by the nodes 3 and 4 after convergence when a = 5, b = 2, c = 1.

3. For node 3:

- A
- B
- AB

Answer :-For Answers Click Here

4. For node 4:

- A
- B
- AB

Answer :-

**For Question 5 and 6 –**

Considering the same payoff strategy as in Table 1 and the following graph G2.

Now, considering b=0 and the divided regions as shown in the figure below, determine the adoption behavior for region (I) and region (IV).

5. For region (I):

- A
- B
- AB

Answer :-

6. For region (IV):

- A
- B
- AB

Answer :-For Answers Click Here

**For Questions 7 to 10 –**

Consider Graph G3. As observed in the system, for a timestamp t, the fraction of people is represented by:

- S
_{t}: Susceptible to infection - I
_{t}: Infected - R
_{t}: Recovered from infection - V
_{t}: Vaccinated against infection. - N: The system’s total population is assumed to be static. N = St + It + Rt + Vt

Additionally, the various relations between the states can be considered.

If the above system reflects one of the models of the current pandemic, then determine the rate equations for the 4 states in the system.

7. 𝛿S/𝛿t

- -α
_{SI }SI + R_{t}τ – φ_{SV }S - α
_{SI}SI – R_{t}τ + φ_{SV}S - -α
_{SI}SI – R_{t}τ + φ_{SV}S - -α
_{SI}SI – R_{t}τ – φ_{SV}S

Answer :-

8. 𝛿I/𝛿t

- α
_{SI}SI + α_{VI}VI + βI - α
_{SI}SI – α_{VI}VI – βI - α
_{SI}SI – α_{VI}VI – βI - α
_{SI}SI + α_{VI}VI – βI

Answer :-

9. 𝛿R/𝛿t

- βI + φ
_{RV}R + Rτ - βI – φ
_{RV}R – Rτ - βI – φ
_{RV}R + Rτ - βI + φ
_{RV}R – Rτ

Answer :-

10. 𝛿V/𝛿t

- φ
_{SV}S + φ_{RV }R – α_{VI}VI - -φ
_{SV}S – φ_{RV}R + α_{VI}VI - φ
_{SV}S – φ_{RV}R – α_{VI}VI - -φ
_{SV}S + φ_{RV}R – α_{VI}VI

Answer :-For Answers Click Here