MO412 - Graph Algorithms and Network Science

 Choose the correct alternative: (I) The social networks, considered a random network, can be modeled by a power law; (II) If you add new nodes to an existing network and add many edges connecting these nodes to high degree's nodes, you end up with bigger hubs, a characteristic of scale-free networks (III) Given a scenario where n = 10000, 2 nodes have k = 1 and 2 nodes have k > 10. This is sufficient to see that we are describing a scale-free network, since there are not many nodes with higher k values and a lot of nodes with lower k values. (IV) In random networks the degrees vary in a large range (V) If all nodes from a given graph have the same degree, it should not be considered a scale-free network or a random network a) I and V are correct; b) II, III and IV are correct; c) II and V are correct; d) I, II and IV are correct; e) None of the above Original idea by André Regino

 Orion was a great warrior of ancient times. It was so important in the Greek history that Zeus created a constellation illustrating him in a fight position. The constellation can be modeled as a graph, with its vertex representing the stars and the edges the links that shape the constellation. Based on the image and the statements below and considering the number o vertex N equals to 15 and that a constellation should never contain a self-loop edge, choose the correct alternative. (I) If Orion's belt is removed (the three star in a row at the bottom of the image), then we have a bipartite graph. (II) The sum of the values of the inverse diagonal of the adjacency matrix is always equal to or higher than the main diagonal in the costellations (III) A spaceship would travel among the constellation using each vertex N without repetition if Orion has lost his shield (IV) A spaceship would travel among the constellation using each edge E without repetition if Orion have lost his shield