## NPTEL Social Network Analysis Week 3 Assignment Answers 2024

1. A network is said to follow small-world property if:

- Average path length α (log(network size))-1
- Average path length α (exp(network size))-1
- Average path length α log(network size)
- Average path length α exp(network size)

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2. A giant component appears in a random network when the average degree of the network is:

- greater than or equal to 0.5
- less than or equal to 0.5
- less than or equal to 1
- greater than or equal to 1

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3. Erdos-Renyi Random Network

- High clustering coefficient
- Small world property
- Degree distribution following power law

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4. Watts-Strogatz Model

- Small world property
- Degree distribution following power law
- High clustering coefficient

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5. Barabasi-Albert Model

- Small world property
- High clustering coefficient
- Degree distribution following power law

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6. The clustering coefficient of a node is not (multiple-choice):

- Independent of p
- Dependent on p
- Dependent on the node’s degree
- Independent of the node’s degree

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7. The principle of preferential attachment can also be thought of as:

- Rich attracts rich
- Poor gets richer
- Rich gets richer
- Rich gets poor

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8. What are the different regimes in the plot below that characterize a random network?

- I: Supercritical regime; II: Critical point; III: Subcritical regime; IV: Connected regime
- I: Connected regime; II: Critical point; III: Supercritical regime; IV: Subcritical regime
- I: Subcritical regime; II: Critical point; III: Connected regime; IV: Supercritical regime
- I: Subcritical regime; II: Critical point; III: Supercritical regime; IV: Connected regime

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9. What characteristic of the Barabási-Albert (BA) model distinguishes it from other random graph models?

- Each new node connects to a fixed number of existing nodes based on the node degree.
- All nodes have the same number of links.
- New nodes are added at random without preference.
- Nodes can be removed and added back into the system.

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10. Based on the following formula for the clustering coefficient of a Watts-Strogatz model, determine the minimum and maximum values of CCWS, given that each node is connected to k/2 forward and k/2 backward nodes.

CC_{WS} = 3(k-2)/4(k-1)

- 3/4, 3/8
- 0, 3/4
- 2, Infinity
- 3/4, 3/4

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