2023-199

The following network represents computers and their connections in a distributed system. The communication between computers flows through the links in any direction.

The system started presenting performance issues.  After some investigation, the cause was attributed to node communication bottlenecks. By looking at the network, which one of the options presents both a reasonable bottleneck cause and a reasonable solution to it?

1. Node 6 has a high clustering coefficient, which indicates a network vulnerability for failures. By removing node 6, the system communication should improve.
2. Node 4 may be overloaded since many nodes depend on it to communicate with each other. By adding link (3,4), performance should improve.
3. Link (3,5) may be overloaded, since it is a bridge and if removed, two connected components are created. By adding link (2,6), performance should improve.
4. The network diameter is 5, as witnessed by the path {(2,1), (1,3), (3,5), (5,7), (7,8)}, which is too high. By adding link (2,8), performance should improve.
5. None of the above

Original idea by: Christian Konishi

2023-198

Consider the Following Applications of the BFS Algorithm starting at the Orange Node:

Which examples are applying BFS the wrong way:

A) B and C

B) B and D

C) A and D

D) Only C

E) None of the above

Original idea by: Arthur Hendricks.

2023-197

Considering the four directed graphs in the following figure:

Which of them are strongly connected and have a diameter 4:

1. III and IV
2. only III
3. only II
4. I and II
5. none of above

Original idea by: Anderson Nogueira Cotrim

2023-196

 Given the following projections of a bipartite network :

Which of the options below provides a possible network that generated these projections? 

1. 1
2. 2
3. 3
4. 4
5. None of the above

Original idea by: Hitalo Cesar

2023-195

 Consider the ten-node graph and the degree distribution plot in the following figures:

Fig. A

Fig. B

The degree distribution plot shown in Fig. B was generated after removing a single link from the graph in Fig. A. Which of the following alternatives correctly identifies potential link(s) that could have been removed to produce that degree distribution?

1. BC or FH
2. BD or DF or FG
3. BE or DF or FG
4. IJ
5. none of above

Original idea by: Anderson Nogueira Cotrim

2023-194

Consider the bipartite network in which the nodes are animals and the nodes are environments. If an animal \( a \) lives in an environment \( e \), then there is a link between \( a \) and \( e \). Take the following image as an example of part of this network.

If a scientist wants to know possible interactions among animals, they need to know which ones live together. One way to determine this it to:

1. Get all nodes of \( A \); only the ones with the same degree live in the same environment
2. Calculate the probabilistic distribution \( p_k \) of degrees; if \( p_k \) is the same for two values \( k_1 \) and \( k_2 \), then the nodes of \( A \) with degree \( k_1 \) live together with the ones of degree \( k_2 \)
3. Calculate the projection on \( A \); if two animal nodes are connected in the projection, then they share the same environment
4. Check which nodes of \( A \) are connected; if they are, they share the same environment
5. None of the above

Originasl idea by: Christian Konishi

2023-193

Given the graph in the figure below, evaluate the assertions:

graph Rede {

A -- B [label="10 Gbps"]

A -- C [label="10 Gbps"]

B -- D [label="10 Gbps"]

B -- E [label="100 Mbps"]

E -- C [label="100 Mbps"]

H -- F [label="10 Mbps"]

E -- F [label="100 Mbps"]

F -- G [label="100 Mbps"]

C -- F [label="10 Mbps"]

B -- G [label="10 Mbps"]

D -- H [label="1 Gbps"]

A -- E [label="100 Mbps"]

E -- H [label="1 Gbps"]

}

view raw Rede.gv hosted with ❤ by GitHub

1. There are two paths from router 'A' to router 'H' that are identical in maximum speeds and same path lenght.
2. The average degree of this graph is 3.25.
3. 32.5% of the nodes have a degree of 3.
4. The fastest path between router 'A' and router 'G' has a bandwidth capacity of 100 Mbps.
5. The graph's adjacency matrix is not symmetric.

Choose the alternative listing the true statements:

1. I, IV and V
2. II, and IV
3. II,III and IV
4. III and IV
5. None of above

Original idea by: João Marcos