Expected Force Centrality

The Expected Force (Lawyer 2015, equation 1) is the entropy of the onward spreading potential after two transmission events from a seed node. Each ordered sequence of two transmissions gives an infected cluster of three nodes with $D_k$ edges to susceptible nodes, and with natural logarithms $$ExF_i = -\sum_k \frac{D_k}{\sum_l D_l} \log \frac{D_k}{\sum_l D_l}.$$

Usage

centrality_expected_force(x, ...)

Arguments

x: Network input accepted by centrality.
...: Further arguments to centrality, such as normalized (divide by the maximum, default FALSE).

Value

A named numeric vector with one score per node, in input node order.

Details

The measure is computed on the simple unweighted network with direction kept, so weights, loops and parallel edges are ignored. In a directed network only outgoing arcs transmit and count toward $D_k$. Different orders of the same two infections count as distinct sequences. A node that cannot start two transmissions scores zero, so isolated nodes and nodes of components with at most three nodes score zero. When every cluster has no edge to a susceptible node the entropy is undefined, and the score is set to zero.

References

Lawyer, G. (2015). Understanding the influence of all nodes in a network. Scientific Reports, 5, 8665. doi:10.1038/srep08665 .

Examples

centrality_expected_force(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>   1.757135   3.519437   2.075442   2.616095   1.584171   2.584102   2.661920 
#>   Evaluate     Create      Share 
#>   2.545039   3.025467   2.689061