HenriqueCampos

Given a graph in which 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 is  false ? a)  Each school corresponds to a clique in the graph and, consequently, may correspond to a community. b)  Suppose there are two schools, A and B, with no students in common initially. School A has  N N  students, and school B has  N − 1  students. If one student moves from A to B, that student will belong to the weak community associated with A and to the weak community associated with B, but will not belong to the strong community associated with either A or B. c)  In general, analyzing only the graph is sufficient to uniquely identify the communities corresponding to schools, regardless of how students move between schools over time. d)  If we extend the network so that two students are connected whenever they kn...

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.