Harmonic Centrality

Harmonic centrality (Marchiori and Latora 2000) sums the inverse shortest-path distances from a node to the other nodes: $$H(i) = \sum_{j \ne i} \frac{1}{d_{ij}},$$ with $1/\infty = 0$, so the score is defined on disconnected networks (Boldi and Vigna 2014). centrality_inharmonic() and centrality_outharmonic() are the mode = "in" and mode = "out" forms.

Usage

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

centrality_inharmonic(x, ...)

centrality_outharmonic(x, ...)

Arguments

x: Network input accepted by centrality.
mode: Direction for directed networks: "all" (default), "out" or "in".
...: Further arguments to centrality. The measure uses invert_weights (default NULL, which inverts for tna input only), alpha (inversion exponent, default 1), cutoff (largest distance counted, default -1 for no limit) and normalized (default FALSE).

Value

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

Details

Edge weights are read as distances, and invert_weights = TRUE converts a weight $w$ to the distance $1/w^\alpha$. weighted = FALSE uses hop counts. mode = "all" treats edges as undirected, "out" uses distances from the node and "in" distances to it. The scores equal igraph::harmonic_centrality() on the weighted graph. normalized = TRUE divides the scores by $n - 1$, as igraph::harmonic_centrality(normalized = TRUE) does.

References

Marchiori, M., & Latora, V. (2000). Harmony in the small-world. Physica A, 285(3-4), 539-546. doi:10.1016/S0378-4371(00)00311-3 .

Boldi, P., & Vigna, S. (2014). Axioms for centrality. Internet Mathematics, 10(3-4), 222-262. doi:10.1080/15427951.2013.865686 .

Examples

centrality_harmonic(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>   58.05676   42.51660   56.48948   33.66818   63.71353   30.68703   50.87966 
#>   Evaluate     Create      Share 
#>   45.01176   45.82217   29.83552