Diffusion Centrality

Diffusion centrality has two forms, chosen by diffusion_method. The "kandhway_kuri" form (Kandhway and Kuri 2014) adds the degrees of a node's neighbors to its own degree, both scaled by \(\lambda\): \(DC(v) = \lambda k_v + \lambda \sum_{u \in N(v)} k_u\). The "power_series" form sums the rows of the first \(n\) powers of the weight matrix: $$DC(v) = \sum_{w} \left( W + W^2 + \cdots + W^n \right)_{vw}.$$

Usage

centrality_diffusion(x, mode = "all", lambda = 1, ...)

Arguments

x

Network input accepted by centrality.

mode

For directed networks: "all" (default), "out" or "in".

lambda

Scale factor \(\lambda\) of the "kandhway_kuri" form. Default 1.

...

Further arguments to centrality. The measure uses diffusion_method ("kandhway_kuri" or "power_series", default NULL, which picks by input type) and loops (default TRUE, FALSE for tna input).

Value

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

Details

The default is "kandhway_kuri", and "power_series" for tna input. The "kandhway_kuri" form uses binary degrees, so edge weights are ignored, and mode sets both the degrees and the neighbor set. On a directed network mode = "all" uses total degrees and the undirected neighbor set. lambda multiplies every score. The "power_series" form uses the edge weights, or ones with weighted = FALSE, and ignores mode and lambda. With loops = FALSE the diagonal of \(W\) is set to zero. The "power_series" values match tna::centralities(measures = "Diffusion").

See also

centrality_expected, centrality_diffusion_centrality, centrality.

Examples

centrality_diffusion(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>         36         42         49         40         34         37         31 
#>   Evaluate     Create      Share 
#>         39         44         40