Considering the Barabási–Albert model, mark the correct alternative regarding growth and preferential attachment. The probability values are rounded to two decimal places.

A) Node M is the node with the highest probability of receiving a link from a new node, of 0.13.

B) Node D is the node with the second highest probability of receiving a link from a new node, of 0.10.

C) Nodes A, C, L, P, and I have the same probability of receiving a new link, of 0.02.

D) Nodes N and E have the same probability of receiving a new link, of 0.08.

E) Nodes H and D have different probabilities of receiving a new link, of 0.08 and 0.09 respectively.

A) F F T T F

B) T F T T F

C) T T F F T

D) T F T F T

E) None of the above

Original idea by: Carolina Albuquerque

Consider a real scale-free network of cellular signaling where the nodes are proteins and the links are interactions between them. Mark the INCORRECT alternative about this network.

a) This network is finite.

b) This network has a degree distribution with a power-law tail.

c) This network will likely exhibit scale-free behaviour, meaning there is no characteristic scale for fluctuations.

d) In this network, most proteins will show high connectivity and can be considered hubs.

e) None of the above.

Based on what has been presented about random graphs in class, correctly identify whether each statement is True (T) or False (F).

1. There is no network in nature that we know of that would be described by the random network model.

2. Edges are independent and have the same probability p. 

3. The clustering coefficient of random graphs is small.

4. The study of random graphs is NOT useful to understand real systems. 

5. Random graphs can develop a giant connected component once the edge probability passes a critical threshold.

a) F  V  V  F  V 

b) V  V  V  F  F

c) V  V  V  F  V

d) V  F  F  V  F

e) None of the above

The Health Department of the imaginary region Scarlet is preparing contingency plans for a potential pandemic. To ensure efficient allocation of resources, they want to determine:

1. Which city would serve as the most effective distribution center for medication, guaranteeing accessibility to the largest number of other cities in the shortest time.

2. Which city would serve as the most strategic location for establishing a blockade, in order to minimize the potential spread of infection to other cities within the network?

Considering the graph below, where each node represents a city and the only means of connection between them is via roads represented by the edges, which cities represent the best candidates for these roles?

A) City 5 as the distribution center and City 4 as the blockade

B) City 3 as the distribution center and City 3 as the blockade

C) City 5 as the distribution center and City 3 as the blockade

D) City 3 as the distribution center and City 4 as the blockade

E) None of the above 

Original idea by: Carolina Albuquerque