[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