Quiz Question – Network Flow

2022-013

Consider the graph below and the flow from 1 to 10, where the capacity value is defined in each link.

Select the correct alternative with the maximum flow of the network and the possible flow values from node 1 to nodes 2, 3, and 4.

$$

1. The maximum flow of the network is 19 and the flow values from node 1 are 8, 5, and 9.
2. The maximum flow of the network is 18 and the flow values from node 1 are 7, 5, and 6.
3. The maximum flow of the network is 20 and the flow values from node 1 are 7, 5, and 8.
4. The maximum flow of the network is 19 and the flow values from node 1 are 7, 5, and 7.
5. None of the above.

Original idea by: Rubens de Castro Pereira

Quiz Question – Communities

2022-012

$$

To uncover the community structure of networks, we can use hierarchical clustering algorithms, and dendrograms help us to extract the underlying community organization. Analyze the figure below, observing the colored lines (A, B, and C) that cut the dendrogram to define communities.

Select the correct alternative:

$$

1. Line A (red) produces three communities: (c1): 6, 9, 13; (c2): 1, 8, 3, 14, 7, 2, 11, 15; (c3): 5, 16, 10, 4, 12, 17. 
2. Line B (green) produces six communities: (c1): 6, 9, 13; (c2): 1, 8; (c3):  3, 14, 7; (c4): 2, 11, 15; (c5): 5, 16, 10; (c6): 4, 12, 17.
3. Line C (brown) produces eleven communities: (c1): 6, 9, 13; (c2): 1; (c3): 8; (c4): 3; (c5): 14; (c6): 7; (c7): 2; (c8): 11; (c9): 15; (c10): 5, 16, 10; (c11): 4, 12, 17.
4. All statements are correct.
5. None of the above.

Original idea by: Rubens de Castro Pereira

Quiz Question – Network Robustness

 2022-011

 

Related to the Percolation Theory and Cascading Failures, analyze the statements below: 

1. Percolation theory shows that the percolating cluster occurs when it is possible to observe a phase transition from many small clusters to a percolating cluster that percolates the whole lattice.

2. The branching model is one of the cascading failures where the node whose initial failure triggers the avalanche of the tree's root and its branches are the nodes whose failure was triggered by this initial failure.

3. The failure propagation model is frequently used to describe cascading failures in networks where a healthy node i changes its state if a φ fraction of its neighbors have failed.

4. The failure propagation models predict the existence of a critical state in which the avalanche sizes follow a power law, and the avalanche exponent α is uniquely determined by the degree exponent of the network on which the avalanche propagates.

Select the correct alternative:

$$

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

Original idea by: Rubens de Castro Pereira