NPTEL Social Networks Week 11 Assignment Answers 2024

1. In Stanley Milgram’s famous small-world experiment, participants were asked to send a letter to a target individual using only acquaintances. What was a key finding of this experiment?

Most letters reached the target individual through a direct connection within three steps
The average number of steps required to reach the target individual was around 6, demonstrating the small-world phenomenon
Participants found that there was no measurable average number of steps to reach the target
The letters typically reached the target individual through a network of over 100 steps

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2. Suppose each of your 50 friends has 30 friends (excluding you). Each of those friends also has 30 friends (excluding them), and this pattern of each having 30 friends continues. How many people can you reach at level i (where Level 1 refers to your direct friends, Level 2 refers to your friends’ friends, and so on)?

30ⁱ
50+30ⁱ
50+30ⁱ⁻¹
50×30ⁱ⁻¹

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3. Imagine you work in a company where most of your close connections are with colleagues from your own department. However, you occasionally attend industry conferences where you meet people from different companies and countries, building new, distant connections. According to Watts and Strogatz, which of the two phenomena are responsible for creating small-world networks?

Your close colleagues frequently form connections among themselves (triadic closure), while your occasional contacts at conferences represent weak ties.
Your colleagues form a tightly-knit group (community structure), while new connections are created within smaller subgroups (triadic closure).
You tend to connect with nearby colleagues due to shared work (homophily), while meeting distant professionals at conferences forms weak ties.
Your work department (a focus of shared activity) brings people together (foci closure), while you tend to form connections with similar colleagues (homophily).

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4. Alex creates a social network graph on NetworkX by forming a 2D grid where each person is connected to their immediate neighbors. After constructing the grid, Alex randomly reconnects some of these relationships with a probability of 0.02. What is the expected average path length between any two people in this network?

Answer :-

5. In a network of friends, the distance between Jordan and Taylor is 25. If the network is built using the Watts-Strogatz model with k=2, what is the probability that Jordan and Taylor are connected through a weak tie?

1
0.01
0.04
0.0016

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6. In a professional network, suppose Ravi wants to connect with Priya through the shortest path. Ravi has four colleagues: Aarti, Manoj, Sunil, and Meera. The distances from each colleague to Priya are as follows: Aarti is 8 steps away, Manoj is 3 steps away, Sunil is 7 steps away, and Meera is 5 steps away. If Ravi uses a decentralized approach to find the shortest path to Priya, which immediate colleague should he choose?

Aarti
Manoj
Sunil
Meera

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7. Consider a social network where initially, each person is connected to their immediate neighbors in a 1-D grid. To introduce some randomness, the network applies a random rewiring process with a probability of 0.03. This means that each connection between two neighbors has a 3% chance of being rewired to connect with a random person in the network. What impact does this random rewiring have on the network?

It increases the average path length by creating more local connections
It has no effect on the average path length as the network remains a regular grid
It decreases the average path length by introducing shortcuts and creating a small-world effect
It decreases the number of connections in the network, making it less connected

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8. In a 2-D Watts-Strogatz model, which of the following is the ideal value of clustering exponent for an efficient decentralized search?

-1
0
1
2

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9. Consider a large online marketplace where each seller is connected to local buyers and a few random buyers across the platform to facilitate quicker connections. If this marketplace represents a small-world network, what is the typical average distance between any two random sellers?

n
log n
n log n
log n²

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10. Imagine you are part of a local sports club (Cluster ‘A’) with many teammates. You also discover another club (Cluster ‘B’) that has a lot of team members who know each other well. When you meet someone from Cluster ‘B’ and become friends with them, this new friendship illustrates: