Figure 5
From: Uncovering nodes that spread information between communities in social networks
An S-I epidemic simulated on the networks of 3 connected communities and the Zachary Karate club. We test the ability of BVA and betweenness to prevent spread in an S-I epidemic. A single node at random is chosen as the initial infected node and the simulation is run until all nodes in the network are infected or there is no further spread after 100 iterations. The simulations are run 300 times and the average percentage of the network infected at each iteration is plotted. The results for each situation are shown up to the iteration number there was on average a increase in the network infected where the maximum permitted was 60. In subfigure (a) the graph of Figure 2 is used for the S-I simulation. The first subplot shows the results of the simulations using a uniform transmission probability of 0.2 in a black line, in blue the results of removing the top 10 nodes which BVA gave the highest score to, and in red the results of removing the top 10 nodes which betweenness produced. In the second subplot in black is the results of using a uniform transmission probability of 0.2, the blue line the results of giving only the top 10 BVA nodes a probability of 0.01 of becoming infected, and the red line where the top 10 betweenness nodes become infected with 0.01. We can see in both plots that BVA and betweenness target nodes which assist slowing down the spread. In subfigure (b) we see the results of the same simulations using the network of communities shown in Figure 3 produced using preferential attachment. With the case of removal both BVA and betweenness significantly reduce the spread and restrict the ability of the spread through the whole network. In the last subplot the rate of infecting the whole network is also significantly reduced although the simulation do not terminate as with the situation of removal. Subfigure (c) shows the epidemic simulation using the Zachary Karate club network presented in Figure 4 with nodes scaled according to the BVA score. The plot shows the results of giving the top 3 BVA and betweenness scored nodes the same reduced probability of infection. The reduced rate of infection is visible for this network as well.