Leverage Centrality

Leverage centrality (Joyce et al. 2010) compares the degree of a node with the degrees of its neighbors: $$l_i = \frac{1}{|N(i)|} \sum_{j \in N(i)} \frac{k_i - k_j}{k_i + k_j}.$$ Positive values mark nodes with more ties than their typical neighbor.

Usage

centrality_leverage(x, mode = "all", ...)

Arguments

x: Network input accepted by centrality.
mode: Direction for directed networks: "all" (default), "out" or "in".
...: Further arguments to centrality.

Value

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

Details

Edge weights are ignored. mode selects both the degree and the neighbor set, and with mode = "all" on a directed network the degree is in plus out. The score lies between -1 and 1. An isolated node is NaN. On undirected networks the values equal centiserve::leverage().

References

Joyce, K. E., Laurienti, P. J., Burdette, J. H., & Hayasaka, S. (2010). A new measure of centrality for brain networks. PLoS ONE, 5(8), e12200. doi:10.1371/journal.pone.0012200 .

Examples

centrality_leverage(regulation_net)
#>      Explore         Plan      Monitor        Adapt      Reflect      Discuss 
#>  0.002797203  0.102719503  0.160858189  0.039826840  0.047792208 -0.121212121 
#>   Synthesize     Evaluate       Create        Share 
#> -0.251515152 -0.149184149  0.070085470 -0.059340659