Quiz Question – Evolving Networks

2022-009

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In many real networks, node deletion can occur at any moment of the network lifecycle. Depending on the number of nodes and links removed, this can impact some network properties. To explore the impact of node deletion, consider a Barabási-Albert model where in each time step, we add a new node with m links, and with rate r, we remove a node. 

Analyze the following statements about node deletion:

1. If r < 1, the number of removed nodes will be greater than the number of new nodes, and the network will be into a random network regime.
2. If r = 1, nodes arrive and are removed at the same rate, and the network has a fixed size and remains scale-free.
3. If r > 1, the number of removed nodes will be less than the number of new nodes, and the network continues to grow and remain with its scale-free properties.
4. The rate r of node deletion does not affect the network topology because the topology is independent of adding and deletion nodes.

Select the correct alternative:

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1. Only statements 1, 2, and 3 are correct.
2. Only statements 2, 3, and 4 are correct.
3. Only statements 1, 3, and 4 are correct.
4. Only statement 4 is correct.
5. None of the above.

Original idea by: Rubens de Castro Pereira