MO412

 Given a network with a defined community division, which has positive modularity, choose the correct alternative: a) Removing an edge from the network will reduce the modularity. b) Merging two different communities into one will increase the modularity. c) Removing an edge between nodes in different communities will increase the modularity. d) Adding an intra-community edge to the network will necessarily increase the modularity. e) None of the above. Original idea by: João Pedro Carolino Morais

 Choose the correct alternative for a scale-free network with power-law exponent γ: a) If γ is 2.5, the giant component is immune to node removal, even if nodes are removed in decreasing order of degree. b) If γ is 4, the network remains connected until almost all nodes are removed at random. c) If γ is exactly 4, there is a fraction of randomly removed nodes that will break the network apart. d) If γ is 3.5, removing the highest-degree nodes first is no more damaging than removing nodes at random. e) None of the above.