HenriqueCampos

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