This centrality measure combines pure topolgical features of the network (node betweenness) with a user-defined node property called Percolation State. The Percolation State defines a source of any kind, and the Percolation Centrality ranks all the nodes according to their ability to transfer or transport this source though the network. Obviously, the Percolation Centrality depends strongly on the chosen Percolation State of the nodes, which must be provided by the user.
|Node percolation state*||text||Compulsory||Percolation State of every node. Should be a positive number.|
|Distance||text||None||Link property acting as weight for the distance calculations. Must be positive numbers.|
* Required Field
An example of usage would be the study of fire spreading in a forest. Imagine that trees are nodes, and two trees are linked when the fire can jump from one to another. Given that some trees are initially burning (their percolation state would be 1.0, non-burning-trees would have 0.0), the percolation centrality of any tree would be its ability to spread the fire through the forest. So, if you are a fireman, you should focus on trees with high Percolation Centrality. This centrality can also be used in the field of rumor or information spreading in social networks.
The following example shows a social network with the initial Percolation State (left) and the Percolation Centrality (right). As usual, warm colors indicate large values. We observe that the Percolation State is focused in one cluster, and that the Percolation Centrality highlights nodes that are bridges between groups (high betweenness) and also emphasizes nodes that are close to the source. Some small nodes that are marked with a red line are nodes with medium-high centrality that are not easy to find by visual inspection.