Figure 1.
Note that in (a), the nodes in the right side of the network and
have high percolation states, whereas in (b), the nodes in the left side of the network
,
and
have high percolation states. The sizes of the nodes correspond to their percolation centrality values.
Figure 2.
Betweenness and percolation centrality profiles of the Alberta model network with , with node sizes matching the centrality values.
(a) The betweenness centrality of nodes; independent of time. (b) The percolation centrality of nodes at . (c) The percolation centrality of nodes at
. (d) Percolation centrality of nodes at
. The infected nodes are highlighted in red.
Figure 3.
The number of percolated nodes, as well as the ratio of average PC and BC values, over time, for the Alberta model network.
As the percolation becomes universal, this ratio settles around unity, as PC converges to BC for each node.
Figure 4.
The number of fully percolated nodes, and the ratio of average PC and BC values over time, for a scale-free network with .
As the percolation becomes universal, this ratio settles around unity, as PC converges to BC for each node.
Figure 5.
A typical run of the simulation, at timestep , for a scale-free network with
.
The Figure shows the ratios against node ID. It could be noted that for some nodes, the PC is more than three times higher than the BC. The ratio is shown as zero if the betweenness of the node is zero.
Table 1.
A comparison between the average timesteps taken for saturation of percolation when the intervention is PC based, BC based or hop distance based. the network used was a scale-free network with .
Table 2.
A comparison between the average timesteps taken for saturation of percolation when the intervention is PC based, BC based or hop distance based. the network used was a random network with .
Figure 6.
Scale-free network: the ranges of and
for which the various centrality measures show the best performance.
This figure corresponds to Table 1. Red: best performance by betweenness centrality based intervention (%). Green: best performance by percolation centrality based intervention (
%). Blue: best performance by hop distance based intervention (
%). Intermediate colours represent ties (
%).
Figure 7.
Random network: the ranges of and
for which the various centrality measures show the best performance.
This figure corresponds to Table 2. Red: best performance by betweenness centrality based intervention (%). Green: best performance by percolation centrality based intervention (
%). Blue: best performance by hop distance based intervention (
%).