Information Centrality

Information centrality (Stephenson and Zelen 1989) measures the information carried by all paths between a node and the others, each path weighted by its length. With $C = B^{-1}$, where $B$ has diagonal $1 + s_i$ ($s_i$ the strength) and off-diagonal entries $1 - w_{ij}$, $$I_i = \frac{1}{C_{ii} + (T - 2R_i)/n},$$ where $T$ is the trace of $C$ and $R_i$ the sum of row $i$.

Usage

centrality_information(x, ...)

Arguments

x: Network input accepted by centrality.
...: Further arguments to centrality. The measure uses weighted (default TRUE).

Value

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

Details

The network is symmetrized with $(w_{ij} + w_{ji})/2$, so direction is ignored. Edge weights enter as tie strengths, and weighted = FALSE uses the binary matrix. Isolated nodes score 0 and are left out of $n$. When the other nodes do not form one connected component, or $B$ is singular, every score is NA with a cograph_undefined_measure warning. On unweighted undirected networks the values equal sna::infocent().

References

Stephenson, K., & Zelen, M. (1989). Rethinking centrality: Methods and examples. Social Networks, 11(1), 1-37.

Examples

centrality_information(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>  0.3947689  0.4512245  0.4449921  0.4508582  0.3776635  0.4159092  0.2730538 
#>   Evaluate     Create      Share 
#>  0.4250643  0.4172676  0.4531011