Laplacian Centrality

Laplacian centrality (Qi et al. 2012) is the drop in the Laplacian energy of a network when a node is removed. Without edge weights the drop is $$L(v) = k_v^2 + k_v + 2 \sum_{u \in N(v)} k_u.$$

Usage

centrality_laplacian(x, ...)

Arguments

x

Network input accepted by centrality.

...

Further arguments to centrality. The measure uses normalized (default FALSE).

Value

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

Details

Edge weights are ignored, so the score is the unweighted case of the weighted measure of Qi et al. (2012). On a directed network \(k\) is the total degree, in plus out, and the neighbor sum runs over out-neighbors. A self-loop adds 2 to the degree. On undirected networks the values equal centiserve::laplacian(). normalized = TRUE divides the scores by their maximum.

References

Qi, X., Fuller, E., Wu, Q., Wu, Y., & Zhang, C.-Q. (2012). Laplacian centrality: A new centrality measure for weighted networks. Information Sciences, 194, 240-253. doi:10.1016/j.ins.2011.12.027 .

See also

centrality_degree, centrality_semilocal, centrality.

Examples

centrality_laplacian(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>         66        118         98         72         70         68         62 
#>   Evaluate     Create      Share 
#>         70        106         84