Question 12 - Dendrogram

Applying a divisive algorithm on the network below, we obtain the following dendrogram:

Network 

Dendrogram

Looking at the dendrogram, we establish two cuts creating community partitions. Which partition yields better communities and why? (Values are rounded to 2 decimal places).

1. A, because its modularity is equal to 0.36
2. B, because its modularity is equal to 0.45
3. A, because its modularity is equal to 0.45
4. B, because its modularity is equal to 0.36
5. None of the above.

  Original idea by: Pedro Henrique Di Francia Rosso

Question 11 - The failure!

You have a network of connected hardware components, where each edge means a route of communication between two hardware components (nodes). The network was constructed to represent the graph below:

The datasheet of the hardware components says that once configured for a given number of communication routes, if more than 40% of these communications become broken, the component will likely fail to maintain the other routes. 

Knowing that you have two new spare hardware components (that will not fail for a long time) and, that soon in the future, you expect a failure in any of the hardware components, which components would you exchange for a spare component to mitigate the impact of a failure? 

1. 3 and 11
2. 4 and 3
3. 11 and 4
4. 4 and 9
5. None of the above.

  Original idea by: Pedro Henrique Di Francia Rosso

Question 10 - Big Components

The Kosaraju-Sharir algorithm is an algorithm used to find strongly connected components in a graph.

Applying the algorithm on the graph given above, how many strongly connected components do we find, and what is the size of the biggest component, and the size of the smallest? (respectively)

1. 4, 8, 1
2. 5, 6, 2
3. 6, 5, 1
4. 4, 7, 2
5. None of the above.

  Original idea by: Pedro Henrique Di Francia Rosso