[MO412] Quizz Question 6 - Scale-free Networks

Mark the alternative that best describes true statements about scale-free networks: 

 

a) The degrees of a random network follow a Normal distribution

b) The ubiquity of the scale-free property means that all real networks are scale-free

c) In a scale-free network, the minimum degree have size 10  if the scale-free network has $\gamma = 2$, largest hub size of 340, and number of nodes is 170 

d) In scale-free networks a few highly connected hubs coexist with a large number of small nodes, and the presence of these hubs plays an important role in the system’s behavior

e) None of the above

Original idea by: Levy Chaves

[MO412] Quizz Question 5 - BFS

About Breadth First Search (BFS) mark the alternative that contains all true statements:

I) The data structure used in standard implementations is a Queue  

II) Can be used to find the shortest path from a source vertice to other vertices in an unweighted graph 

III) Can be used to find all connected components in a undirected graph 

IV) The BFS traversal of a graph will result into a Tree

V) We can use BFS to find all the vertices on any shortest path between a given pair of vertices (a, b) by running two BFS: one starting from a, and other starting from b 

a) only I, II, and IV

b) only I, II, and III

c) only II, III, IV, and V

d) only II, III, and V

e) None of the above 

 

 

Original Idea by: Levy Chaves

[MO412] Quizz Question 4

Mark the alternative that corresponds to the following derivates: $f(x) = 5x^{4} + 6x^{3} + 20$, $z(x) = 5x^{5} + \sqrt{x^{3}} - x^{\frac{3}{5}} $, and $g(x) = -\frac{1}{3}x^{15} + \frac{1}{\sqrt{x}} -\frac{3}{\sqrt[3]{x}} $ 

a) $f'(x) = 20x^{3} + 18x^{2}$; $z'(x) = 25x^{4} + \frac{3\sqrt{x}}{2} - \frac{3}{5}x^{-\frac{2}{5}} $;  $g'(x) = -5x^{14} - \frac{1}{2}x^{-\frac{3}{2}} - x^{-\frac{4}{3}}$  

b) $f'(x) = 20x^{3} - 18x^{2}$; $z'(x) = 25x^{4} - \frac{3\sqrt{x}}{2} + \frac{3}{5}x^{\frac{2}{5}} $;  $g'(x) = 5x^{14} + \frac{1}{2}x^{\frac{3}{2}} + x^{-\frac{4}{3}}$  

c) $f'(x) = 20x^{3} + 18x^{2}$; $z'(x) = 25x^{4} + \frac{3\sqrt{x}}{2} + \frac{3}{5}x^{\frac{2}{5}} $;  $g'(x) = -5x^{14} - 1x^{\frac{3}{2}} - x^{-\frac{4}{3}}$  

d) $f'(x) = 20x^{3} + 18x^{2}$; $z'(x) = 25x^{4} - \frac{\sqrt{x}}{2} - \frac{3}{5}x^{-\frac{2}{5}} $;  $g'(x) = -5x^{14} - \frac{1}{2}x^{3} - x^{\frac{4}{3}}$  

e) None of the above

Original Idea by: Levy Chaves

[MO412] Quizz Question 3

Given a network G with N nodes, L links and probability p. Find a formula for that express the probability of a given node i has exactly k links in terms of N, k, p, and the average degree <k>.


a) 
b) 

c ) 

d)  

Original Idea by: Levy Chaves

[MO412] Quizz Question 2

About Depth First Search (DFS) and topological sorting, assign true or false to the following statements:

I) The visited node order of the following graph and adjacency list, starting with s, is s a c e b d

II) While running a DFS on a directed graph, if from vertex u we visit a finished vertex v, then the edge (u, v) is a cross-edge

III) if a topological sort exists for the vertices in a directed graph, then a DFS  on the graph will produce no back edges 

IV) A DFS in a directed graph always produces the same number of tree edges 

V) Suppose we perform a DFS on a directed graph G. If we remove all the back edges found, the resulting graph is acyclic 

a) I, II, III

b) II, III, V

c) I, III, IV, V

d) I, III, V

e) All statements are true

Original Idea by: Levy Chaves

 

[MO412] Quizz Question 1

 

Pedro and Sofia are brothers, and they argue pretty often. Their mother is a lovely and calm person, but today she is stressed out because of her work and has decided to ground them for arguing so often. She left them an exercise to solve to get out of detention. As exercise, their mother drew a graph (image below) and asked her children if the following statements about the graph are true or false: 

I. The edge between nodes BD is a bridge

II. The shortest path between the nodes E and C is 3

III. The graph diameter is 6 

IV. The graph is disconnected

V. By removing the edges BD and EA the resulting graph has two connected components

   

 Your task is to help the kids to mark only the options that contain only the correct statements. Consider that the graph is undirected and each link has weight equal to 1. 

a) only I, II, V are correct

b) only I, III, and IV are correct 

c) only III, and V are correct

d) only II, III, and V are correct

e) None of the above

Original idea by: Levy Chaves