HenriqueCampos

Consider an undirected network composed of several disconnected components, where each component is a clique (a complete graph in which every node is connected to every other node). Assume that the component sizes follow a normal distribution. Observation: The question can be generalized by replacing each clique component with a subgraph exhibiting a high clustering coefficient. a) The network is disassortative, since every edge connects two vertices with the same degree. b) If we assign a direction to every edge in the network, then, regardless of the directions chosen, the resulting directed network will be assortative. c) In this network, r < 0 r < 0 . d) If we take the complement of this network (that is, a network in which an edge exists if and only if it did not exist in the original network), the complement will be assortative, since every small component will become a set of unconnected hubs. e) None of the above. Original idea by Henrique Campos Padula.

 In a growin netwok with attachment probability  Π ( k )  ∝ ka  with α = 1. What of the following statements. a) The probability of a node get a new connection dosn't relate to the degree. b) New connections will be only to nodes with degree 1. c)  The probability of a node get a new connection it's proportional to its degree. d) New connections will be created completly randomly across de nodes. e) None of the above. Original idea by: Henrique Campos Padula

In a growing network with attachment probability Π ( k ) ∝ k α \Pi(k) \propto k^\alpha  , where α =1 , which of the following statements is correct? a) The probability of a node getting a new connection does not depend on its degree. b) New connections are formed only with nodes of degree 1. c) The probability of a node getting a new connection is proportional to its degree. d) New connections are created completely at random across all nodes. e) None of the above. Original idea by: Henrique Campos Padula

Consider a graph in which each node represents a student, and an edge connects two students if they share at least one hobby. At the beginning of the school year (month 0), no two students share any hobbies, so the graph has no edges. As time passes, students interact, become friends, and start sharing hobbies. Once a student adopts a new hobby, they keep it permanently. How does the structure of the graph could evolve over time? Consider snapshots of the graph at months 0, 3, 6, and 9. a) Subcritical → Supercritical → Critical → Connected b) Critical → Supercritical → Supercritical → Connected c) Subcritical → Subcritical → Subcritical → Supercritical d) Subcritical → Connected → Critical → Supercritical e) None of the above. Original idea by: Henrique Campos Padula

Given a graph where each node represents a student and two students are connected by a link if they have ever studied at the same school (not necessarily in the same class or year). Which of the following statements are true? a) A node with clustering coefficient equal to 1 implies that the student never changed schools. b) A complete graph implies that there is just one school. c) A student who never changed schools will have clustering coefficient equal to 1. d) The number of connected components in the graph is necessarily equal to the number of schools. e) None of the above. Original idea by: Henrique Campos Padula