Carlos Trindade's Graph Algorithms Quiz Blog

  Consider the T network below:   Which of the following statements are  true ?   I. T is in supercritical regime because its average degree \(\langle k \rangle = 4.5\) is higher than \(1\).   II. T can't be considered a random network because node G has degree \(k = 7\), representing a hub in the network and its degree is far from \(\langle k \rangle = 3.25\).   III. T is in connected regime, since its average degree is higher than \(\ln N\)   IV. T is a random network with \(N = 8\) nodes and \(p = 0.46\).     A) I and IV B) III and IV C) II and III D) I and II E) None of the above     Original idea by: Carlos Trindade  

 A Distribution Center (DC) is a location where companies or industries store manufactured products with the goal of delivering them to other units or customers. The location of a DC is very strategic, since it must minimize the costs of delivery. Considering the graph below, what is the best location to place a DC, minimizing the expected distance to the other locations?     A) Node D, because it has the lowest average distance among nodes with 5 or more connections, indicating it is the most central high-degree node. B) Node E, because it connects the left cluster (C, D) to the right cluster (F, K) and has an average distance of approximately 1.73. C) Node D, because it has the highest number of direct connections, minimizing the maximum distance to any location. D) Node F, because it has an average distance of approximately 1.54. E) None of the above.   Original idea by: Carlos Trindade