Semi-Local Centrality

Semi-local centrality (Chen et al. 2012) sums, over the neighbors \(u\) of a node and the neighbors \(w\) of each \(u\), the number \(N(w)\) of nodes within two steps of \(w\): $$C_L(v) = \sum_{u \in \Gamma(v)} \sum_{w \in \Gamma(u)} N(w).$$

Usage

centrality_semilocal(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 the neighbors, and with mode = "all" on a directed network a reciprocated tie counts twice. An isolated node scores 0. On undirected networks the values equal centiserve::semilocal().

References

Chen, D., Lu, L., Shang, M.-S., Zhang, Y.-C., & Zhou, T. (2012). Identifying influential nodes in complex networks. Physica A, 391(4), 1777-1787. doi:10.1016/j.physa.2011.09.017 .

See also

centrality_laplacian, centrality_degree, centrality.

Examples

centrality_semilocal(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>        324        369        432        306        306        288        243 
#>   Evaluate     Create      Share 
#>        306        405        369