2024-243

In the evolving network model that includes the concept of fitness, how does a node's fitness influence its ability to gain new connections?

a) Fitness gives all nodes an equal chance to receive new connections, eliminating the advantage of high-degree nodes.

b) Nodes with higher fitness are more likely to receive new connections, even if they currently have a low number of links.

c) Fitness reduces the effect of preferential attachment, favoring nodes with fewer connections.

d) Fitnes only affects the removal of existing links, not the formation of new ones.

e) None of the above.

Original idea by: Sergio Sanchez

2024-242

In the Evolving Networks chapter of Barabasi's book, Network Science, many models for network evolution are presented. For most of these models, which of the following concepts is the starting point to derive degree probability distributions and other characteristics of the networks?

A) Clustering coefficient

B) Preferential attachment

C) Network robustness

D) Shortest path length

E) None of the above


Original idea by: João Augusto Ferreira de Moura

2023-219

The degree correlation function depicted in the following figure (shown in purple) is derived from a Bianconi-Barabási model with parameters N = 10,000, m = 3, and a uniform fitness distribution:

(Extracted from Albert-László Barabási book "Network Science")

Please choose the accurate statement regarding this figure:

1. This network exhibits a neutral nature due to the presence of structural cutoff phenomena.
2. The network cannot be classified as disassortative since randomizing the network while maintaining the same degree distribution produces a similar behavior, as the orange dots (Randomized R-S).
3. While this network displays some disassortativity, it is not pronounced primarily due to structural cutoff.
4. This network does not exhibit any structural cutoff phenomena. 
5. none of above

Original idea by: Anderson Nogueira Cotrim

2023-218

The network below, shown at t=0 with each node and its respective fitness η, follows the Bianconi-Barabasi model and grows by adding a new node at each subsequent time unit, accompanied by two new links (m=2). All new nodes have a fitness of 1. Which node is expected to have the most links at t=1 and at t going to infinity?

1. node 1 at t=1; node 3 at t=infinity.
2. node 2 at t=1; node 3 at t=infinity.
3. node 2 at t=1; node 5 at t=infinity.
4. node 3 at t=1; node 5 at t=infinity.
5. None of the above

Original idea by: Thaysa Bello

2022-178

Consider a network described by the Bianconi–Barabási model, with degree dynamics following a power law.  Consider also a node A joining this network at time t=10 and another node B joining the network at time t=100.  If node B has twice the fitness of node A, at which time point t will the degree of node B start to be greater than or equal to the degree of node A?

1. t = 100
2. t = 1000
3. t = 10000
4. t = 100000
5. None of the above

Original idea by: Meer Muhammad Khan

2022-177

Aging can influence the topology of a network.  Denote by \( \Pi(k_i,t-t_i) \) the probability of a new node arriving at time \( t \) connecting to node \( i \) of degree \( k_i \), where \( t_i \) is the time node \( i \) was added to the network.  Aging can be modeled by choosing \( \Pi(k_i,t-t_i) \sim k_i(t-t_i)^{-\nu} \), where \( \nu \) is a tunable parameter.  In this case, what is not correct to state regarding the tunable parameter \( \nu \):

1. If \( \nu < 0 \), new nodes will link to older nodes.
2. If \( \nu \rightarrow -\infty \) each new node connects to the oldest node.
3. If \( \nu > 0 \) new nodes are encouraged to attach to younger nodes.
4. If \( \nu \rightarrow \infty \) each node will connect to its immediate predecessor.
5. None of the above.

Original idea by: Marcelo Silva

2022-176

You are analyzing a network that follows the Bianconi-Barabási Model. You know that a node A has degree 5 and fitness 0.2, and a node B has degree 16 and fitness 0.5. How much more likely is a new node to connect to B than to A?

1. 2.5 times more likely
2. 3.2 times more likely
3. 8 times more likely
4. 12 times more likely
5. None of the above

Original idea by: Luan Silveira

2022-123

Below are descriptions of Evolving Network models. Select the alternative that correctly relates each description to the named model:

    I. This model generates rather complex degree correlations. It's a possible extension of the preferential attachment model that addresses the low-degree cut-off phenomenon via the inclusion of attractiveness.

    II. This algorithm generates random scale-free networks using a preferential attachment mechanism. The network grows by adding new nodes over time, and these new nodes link to existing nodes in the network with probability proportional to the degree.

    III.  This model also it's a possible extension of the preferential attachment model where we incorporate the role of fitness. In that case , we assume that preferential attachment is driven by the product of a node’s fitness and its degree. Consequently, a node with a higher fitness will increase its degree faster.

    IV. This is a good representation of real networks were average degree s have a high increase on a short time period. In the other models discussed so far, the number of links increases linearly with the number of nodes. In this particular case, the number of links grows faster than N.

    V. This approach intends to replicate the idea of a finite life span, so nodes have a limited lifetime. In these networks, nodes do not disappear abruptly, but fade away throughout, gradually reducing the rate at which they acquire new links. That is done by introducing capacity limitations.

Now mark the correct alternative:

    A. I - Initial attractiveness, II - Barabasi-Albert,  III - Bianconi-Barabási, IV - Accelerated Growth, V - Aging

    B. I - Initial attractiveness, II - Bianconi-Barabási,  III - Barabasi-Albert, IV - Aging, V - Accelerated Growth

    C. I - Bianconi-Barabási, II - Barabasi-Albert,  III - Initial attractiveness, IV - Accelerated Growth, V - Aging

    D. I - Initial attractiveness, II - Bianconi-Barabási,  III - Barabasi-Albert, IV - Accelerated Growth, V - Aging

    E. None of the above

Original idea by: Victória Pedrazzoli

2022-121

Consider the following statements about the Initial Attractiveness model:

I -  Initial attractiveness increases γ, the degree exponent, making the network more homogeneous and reducing the size of the hubs. 

II - Initial attractiveness adds a random component to the probability of attaching to a node. This random component favors the numerous small-degree nodes and weakens the role of preferential attachment

III -  Initial attractiveness enhances the probability that new nodes link to the small-degree nodes, which pushes them towards higher degrees.

IV - The higher the degree of a node, the more relevant its initial attractiveness term gets.

The only statements that are correct are:

A) I, II, and IV.
B) II and III.
C) I, II and III.
D) I, III and IV.
E) None of the above.

Original idea by: Athyrson M. Ribeiro

2022-115

Consider the following statements, regarding the Bianconi-Barabási model.

1. The preferential attachment is driven by the product of a node's fitness, η, and its degree \( k \).
2. A node with a higher fitness will increase its degree faster. 
3. When all fitnesses are equal, the Bianconi-Barabási model reduces to the Barabási-Albert model.
4. The earlier a node joins the network, the larger is its degree at any time.

Choose the best answer.

1. I - True; II - True; III - False; IV - False.
2. I - True; II - False; III - False; IV - True.
3. I - False; II - True; III - True; IV - False.
4. I - True; II - True; III - True; IV - False.
5. None of the above.

Original idea by: Diogo Souza

2021-031

Choose the incorrect alternative below:

1. The Initial Attractiveness model addresses an issue with the Barabási-Albert model, namely, that an isolated node cannot acquire links, by adding a constant to the preferential attachment function.  Instead of just \( k \), we now have \( k + A \).
2. The Internal Links model addresses an issue with the Barabási-Albert model, namely, to add new links among preexisting nodes, and not only among the new node and former nodes.
3. The Accelerated Growth model adds new nodes and links.  The number of links to add is not a constant, but grows over time.
4. In real networks, nodes and links can disappear. The Node Deletion model only removes nodes, and does not add new nodes. Nodes are removed based on a rate \( r \). Depending on \( r \) being positive or negative, more or less nodes are removed.
5. E. None of the above

Original idea by: Mauricio Schiezaro

2021-030

According to the Barabási-Albert model, the ability of a node to acquire more links grows with the node's age. But in reality newer nodes can acquire a large number of links and become hubs, despite their age. To try and explain this behavior, the Bianconi-Barabási model was created. Choose the incorrect alternative regarding this model.

1. A new property of a node is introduced, namely, its fitness, that represents its ability to turn a random link into a permanent link.
2. The new model is composed of two main steps. In the first step, a new node is added in the network with a random fitness.
3. The new model is composed of two main steps. In the second step, links are created using preferential attachment.
4. Preferential attachment in this model is driven by the product of the node's fitness by its degree.
5. None of the above. 

 

Original idea by: Adolfo Aires Schneider

2021-028

 When a Bianconi-Barabási model reduces to a Barabási-Albert model?

1. When the degree distribution is a normal distribution
2. When the fitness distribution is uniformly distributed in the interval [0, 1]
3. When the model generates a power law degree distribution
   
4. When all fitnesses are equal
5. None of the above

Original idea by: Thales Nazatto