Network Science Questions

Given the networks below, which of the following options is most likely correct about them: (Consider r as the degree correlation degree) a) Network A is disassortative, as the hubs tend to connect with other hubs, while Network B is assortative, with hubs tending to connect to nodes of smaller degree. b) Network A is assortative, with a positive  r , and network B is disassortative, with a negative  r. c) Network A is a perfectly assortative network, where each node links only to nodes with the same degree, while network B is disassortative, with hubs preferring to link to low-degree nodes. d) Network A is assortative with a negative  r , and network B is disassortative with a positive  r . e) None of the above  Original idea: Matheus C. Lindino

In real-world networks, nodes can often be removed, such as when research papers are retracted. Based on the node deletion model, which describes the relationship between adding and removing nodes, identify the incorrect statement regarding the behavior of such networks: a) The network maintains a scale-free characteristic if the number of nodes removed is smaller than the number of new nodes added. b) If the rate of node removal exceeds one (r > 1), the network will enter a declining phase. c) The network's degree distribution will shift from scale-free to exponential when the rate of node removal surpasses a critical threshold related to initial attractiveness. d) The network maintains its scale-free nature if the rate of node removal is equal to the rate of node addition. e) None of the above.  Original idea: Matheus C. Lindino