## NPTEL Social Networks Week 9 Assignment Answers 2024

1. Which of the following mechanisms is most likely responsible for the emergence of a power law degree distribution in complex networks?

- Nodes are added with equal probability to all existing nodes.
- Nodes connect randomly without preference to other nodes.
- New nodes preferentially attach to existing nodes with higher degrees.
- All nodes have an equal chance of forming connections.

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2. Given a network G being generated by ‘rich get richer’ phenomenon. Figure 1 shows the snapshot of the network at time t. A new node u enters the network at time t + 1 and makes an edge with one of the existing nodes. What is the probability that node ‘u’ will make an edge with B?

- 1/2
- 1/3
- 1/4
- 1/5

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3. Consider the set E=2,4,6,…,28,30 A value a1 is selected uniformly at random from this set. Then, a second value a_{2} is chosen uniformly at random from the same set. This process is repeated until 10 values, a_{1}, a_{2}, .., a_{10} are selected. The sum S = a_{1} + a_{2} + .. + a_{10} is then calculated. Which of the following ranges represents all possible values that the sum can take?

- [20, 24, .., 300]
- [20, 24, .., 200]
- [10, 24, .., 240]
- [2, 4, .., 300]

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4. In a random graph with 400 nodes and edges between any two nodes with a probability of 0.5, where can one expect the peak of the degree-distribution graph?

- 100
- 200
- 300
- 250

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5. Which of the following is an example of a real-world phenomenon that follows a power law distribution?

- The heights of individuals in a population
- The number of citations academic papers receive
- The distribution of shoe sizes among adults
- The daily temperature in a specific city

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6. According to the power law, the frequency (shown on the y-axis) is inversely proportional to k, where k represents the values plotted on the x-axis. In this relationship, the exponent a is ideally between which values?

- 0,1
- -1, 1
- 1,5
- 2,3

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7. Which of the following statements is true about the Barab´asi-Albert (BA) model for scale-free networks?

- Nodes are added randomly to the network
- The BA model follows a preferential attachment mechanism
- All nodes in the BA model have equal probabilities of forming connections
- New nodes in the BA model are equally likely to connect to any existing node

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8. In the Erdos-Renyi G(n, p) model for random graphs, which of the following statements accurately describes the model?

- The model involves adding a fixed number of edges randomly to a complete graph with n nodes
- Each pair of nodes in a graph with n nodes has a probability p of being connected by an edge, independently of other pairs
- The model constructs a graph by preferentially attaching new nodes to existing nodes with higher degrees
- In this model, the probability p determines the number of nodes added at each step

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9.

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10. Consider the given network K, which of the following nodes does a new node ‘X’ entering the network choose to form an edge according to preferential attachment?

- A
- B
- C
- D
- E
- F

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