MO412 - Thiago Laitz

In the context of epidemic spreading on networks, which statement correctly explains why scale-free networks allow epidemics to spread more easily than random networks? A) Because scale-free networks have a lower average degree ⟨k⟩, making it harder to contain infections. B) Because scale-free networks contain hubs with very high degree, causing ⟨k²⟩ to diverge and making the epidemic threshold λc approach zero. C) Because scale-free networks follow homogeneous mixing, allowing each node the same chance to infect others. D) Because scale-free networks have stronger community structure, slowing down infection and increasing the epidemic threshold.  E) None of the above. Original idea by: Thiago Soares Laitz

Consider the undirected graph shown below. The network contains two dense regions: nodes (1-4) and nodes (5-7), connected through node 3. Node 3 also connects to node 8 through the dashed edge (3,8). We wish to apply the Girvan–Newman divisive community detection algorithm, that is based on the betweenness of nodes. Assume that in the first iteration, the dashed edge (3,8) has the highest betweenness and is therefore removed. After removing the edge (3,8), which of the following statements best describes the next step of the algorithm and its structural implications? A) Since the graph becomes disconnected after removing (3,8), the algorithm terminates immediately and each connected component is taken as a final community. B) The algorithm recomputes the betweenness of all remaining edges. Because node 3 still acts as the bridge between the two dense regions (1–4 and 5–7), the edges incident to node 3 are expected to gain higher betweenness, making edges such as (3,5) or (3,7) the next...