2022-072

In a bipartite network, we can generate a different projection for each disjoint set of nodes. Consider the following bipartite network:

The average clustering coefficient, <C>, for each projection, rounded to two decimal places, would be:

1. <C> = 0,33 for projection on set A, <C> = 0,33 for projection on set B
2. <C> = 0,47 for projection on set A, <C> = 0,25 for projection on set B
3. <C> = 0,67 for projection on set A, <C> = 0,60 for projection on set B
4. <C> = 0,33 for projection on set A, <C> = 0,60 for projection on set B
5. None of the above

Original idea by: Athyrson M. Ribeiro

2022-071

 

Cherepnalkoski and Mozetič published the community structure evaluation of retweet networks related to European Parliament (EP) members in 2016 [1]. They collected one year of data from the behavior of EP members on Twitter. For the record, Tweets are posts on Twitter and retweets are re-posts, or in other words: a retweet is a quick way to share (in a rather public way) something another person said to people that follow you. So the researchers were analyzing on a community level how EP members had behaved on Twitter by sharing posts of each other.

The so-called core retweet network (composed only by EP members) has 459 nodes, 4,441 edges, is represented in the figure below, and has the following structure: 

1. Each node represents one EP member; 
2. Links represent retweets between EP members (when an EP shared something that another EP member posted on Twitter);
3. Node colors represent the political groups of the EP members;
4. Node sizes are proportional to the total number of times that an EP member has been retweeted by other members;
5. Link colors represented the EP member that has been retweeted by the respective colleague.

The core retweet network of the EP members [1]

Evaluate the following statements:

1. This is an undirected network;
2. This is not a weighted network;
3. The graph formed by this network is a complete graph;
4. The average degree is very close to 458.

Select the best answer:

1. 1 - True, 2 - False, 3 - True, 4 - False
2. 1 - False, 2 - True, 3 - False, 4 - True
3. 1 - False, 2 - False, 3 - True, 4 - True
4. 1 - False, 2 - True, 3 - False, 4 - False
5. None of the above

Reference

[1] Cherepnalkoski, D., Mozetič, I. Retweet networks of the European Parliament: evaluation of the community structure. Appl Netw Sci 1, 2 (2016). https://doi.org/10.1007/s41109-016-0001-4

Original idea by: André Portela

2021-070

Consider a disease infecting a population with \( N \) individuals, where \( S(t) \) is the number of individuals that are healthy (susceptible to the disease) at time \( t \), \( I(t) \) is the number of individuals that have been already infected at time \( t \), \( \langle k \rangle \) is the number of contacts that an individual usually has, and \( \beta \) is the rate of transmission.

Under the homogeneous mixing hypothesis, what is the probability that an infected person encounters a healthy individual?

1. \( S(t)I(t) \)
2. \( S(t)/N \)
3. \( I(t)/N \)
4. \( \beta \langle k \rangle S(t) I(t) / N \)
5. None of the above

Original idea by: Leandro Stival

2021-069

Regarding epidemic forecasting, it is correct to state that:

1. the relative times of disease arrival depend only on the degree distribution of the mobility network.
2. the relative times of disease arrival depend only on the clustering coefficients of the mobility network.
3. the relative times of disease arrival depend only on the topology of the mobility network.
4. It is not possible to predict the times of disease arrival just by looking at the mobility network.
5. None of the above.

Original idea by: Sara Mercês

2021-068

Given the two networks (each with 3 different colored partitions) shown in the image below:

1                                           2

Which of the networks has the smallest modularity? What is this value, rounded to two decimal places?

1. Network 1, M = 0.49
2. Network 1: M = 0.41
3. Network 2: M = 0.49
4. Network 2: M = 0.41
5. None of the above

Original idea by: Victor Antonio Menuzzo

2021-067

Suppose that there is a viral epidemic following a classic SIR model in a certain region. What would be the effect of lockdown in this region?

1. It increases the value of \( R_0 \)
2. It reduces the value of the recovery rate, which reduces \( R_0 \)
3. It reduces the average degree, moving out from endemic state
4. It does not affect the current epidemic state
5. None of the above

Original idea by: Matheus Cerqueira

2021-066

Evaluate each of the following statements:

1 - Under random node removal, a random network will break into smaller components in a gradual, linear way.

2 - Scale-free networks, regardless of the degree distribution exponent, are robust against random failures, since their biggest component will only vanish when the fraction of removed nodes gets close to 1.

3 - The breakdown of a scale-free network is the same for random node removal and hub removal.

1. 1-False, 2-False, 3-False
2. 1-True, 2-True, 3-False
3. 1-False, 2-True, 3-False
4. 1-True, 2-True, 3-True
5. None of the above

Original idea by: Thales Rogério