Quizz Question 13

 Considering a network with six nodes, in how many ways we can divide this network into two subgraphs of sizes $N_ {1}$ = $N_{2}$ = $3$ ? 

a) 120

b) 90

c) 58

d) 20

e) None of the above

Original idea by: Levy Chaves

Quizz Question 12

 Below are descriptions of essentials concepts in Network Robustness. Select the alternative that correctly relates each description to the named model

I) Removing several nodes can break a network into several isolated components. Obviously, the more nodes we remove, the higher are the chances that we damage a network. This concept aims to answer the question: "How many nodes do we have to delete to fragment a network into isolated components?" by modelling the process of randomly placing pebbles on an n-dimensional lattice with probability p, and predicts the sudden formation of a single large cluster at a critical probability ${\displaystyle p_{c}}$.

II) This is frequently used to describe cascading failures. It considers a network with an arbitrary degree distribution, where each node contains an agent. An agent can be in the state 0 or 1, and is characterized by a breakdown threshold.

III) This mathematical derivation derives a threshold at which complex networks will lose its giant component. It is derived from the basic principle that in order for a giant component to exist, on average each node in the network must have at least two links

IV) Is related to maintain its basic functions in the presence of internal and external errors. In a network context, it refers to the system's ability to carry out its basic functions even when some of its nodes and links may be missing.

a) I) Molloy-Redd Criterion;  II) Cascade Failures; III) Percolation Theory; IV) Targeted Attacks

b) I) Failure Propagation Model; II) Targeted Ataccks; III) Robustness; IV) Percolation Theory

c) I) Percolation Theory; II) Failure Propagation Model; III) Molloy-Reed Criterion; IV) Robustness

d) I) - Molloy-Redd Criterion; II) - Percolation Theory; III) Failure Propagation Model; IV) - Robustness

e) None of the above

Original Idea by: Levy Chaves

Quizz Question 11

Hello Prof. Medians, this week I decided to change this question published in May, 28, 2022, regarding Network Flows. Thank you. 

 

Quizz Question 10

 Choose the correct alternative about Evolving Networks: 

a) Preferential attachment is the only responsible for the emergence of the scalar-free property 

b) The Evolving Network Models are models that capture the mechanisms that govern the time evolution of a network. The most studied example is the Barabási-Albert model.

c) The Barabási-Albert model also consider the case of acquiring new links in its original formulation 

d) The Node Deletion Model admits three distinct phases: Sublinear, Critical, and Exponential. 

e) None of the above

Original Idea by: Levy Chaves

[MO412] Quizz Question 09 - Network Flows

Consider the statements in below about network flows:  

 

I) The maximal flow in the following network is 10 

II) Given the following graph with its corresponding max flow and capacities from s to t 

 

The residual graph associated to the above solution is the following:  

III) The push-relabeled based algorithms are the ones which involves computing a residual network and looking for augmenting paths

IV) The sum of the incoming flow of a vertex u has to be equal to the sum of the outgoing flow of u, except in the source and sink nodes 

Given these statements, mark the alternative that all statements are true:

a) only I, and IV 

b) only III, and IV

c) only II, and III

d) only I, II, and IV

e) None of the above 

Original idea by: Levy Chaves

[MO412] Quizz Question 08 - Barabási-Albert Model

Considering a Barabási-Albert network with $10^{3}$ nodes and $m=4$. Choose the alternative that describe the average degree, diameter, and clustering coefficient, respectively. Round up two decimal places: 

 

a) Avg. Degree = 8, Diameter = 3.90, Clustering Coeff. = 0.48  

b) Avg. Degree = 8, Diameter = 3.57, Clustering Coeff. = 0.05

c) Avg. Degree = 4, Diameter = 5.48, Clustering Coeff. = 0.09

d) Avg. Degree = 8, Diameter = 3.57, Clustering Coeff. = 0.50

e) None of the above. 

Original idea by: Levy Chaves 

[MO412] Quizz Question 7

Hello Prof. Medians, this week I decided to change this question published in April, 20, 2022, regarding BFS. Thank you.