Modified Expected Force centrality

Multiplies the two-event Expected Force by the logarithm of alpha times seed degree (Lawyer 2015, equation 2). Alpha defaults to two, as in the paper, and must be finite and strictly greater than one. Directed input uses outgoing degree, consistent with the outgoing transmission process. An isolate scores zero without evaluating the logarithm of zero. All graph, event-counting and zero-force conventions of centrality_expected_force apply. Native log addition avoids overflow when alpha times degree cannot be represented.

Usage

centrality_modified_expected_force(x, exf_alpha = 2, ...)

Arguments

x

Network input accepted by centrality.

exf_alpha

Degree rescaling factor, default two, finite and greater than one. The paper motivates small values; larger finite values are permitted by the formula without a predictive-performance claim.

...

Additional arguments to centrality. normalized = TRUE divides by the maximum score; all-zero results remain zero.

Value

Named numeric vector in input node order.

References

Lawyer, G. (2015). Understanding the influence of all nodes in a network. Scientific Reports, 5, 8665, equation 2. doi:10.1038/srep08665 .

Examples

centrality_modified_expected_force(igraph::make_graph("Zachary"))
#>         1         2         3         4         5         6         7         8 
#> 19.634822 13.579674 14.822717 10.462639  5.717804  7.021545  7.021545  8.028485 
#>         9        10        11        12        13        14        15        16 
#>  9.853701  4.534737  5.717804  1.871167  4.251166  9.805879  4.636217  4.636217 
#>        17        18        19        20        21        22        23        24 
#>  2.539017  4.423686  4.636217  6.771364  4.636217  4.423686  4.636217  9.103169 
#>        25        26        27        28        29        30        31        32 
#>  4.730017  4.846594  4.192057  7.716535  6.364664  7.787481  8.118877 10.690913 
#>        33        34 
#> 16.382792 20.290653