Diffusion Centrality

Sum of scaled degrees of a node and its neighbors, measuring the node's potential for spreading information through the network.

Usage

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

Arguments

x

Network input (matrix, igraph, network, cograph_network, tna object).

mode

For directed networks: "all" (default), "in", or "out". Only used when diffusion_method = "kandhway_kuri" (the default for non-tna inputs); ignored under "power_series", which always treats the matrix as the row transition operator.

lambda

Scaling factor for neighbor contributions. Default 1. Only used when diffusion_method = "kandhway_kuri".

...

Additional arguments passed to centrality (e.g., diffusion_method, loops, weighted, directed).

Value

Named numeric vector of diffusion centrality values.

Details

Two methods are supported. "kandhway_kuri" (Kandhway & Kuri, 2014) computes the 1-hop binary-degree neighborhood sum and is the default for raw matrices, igraph objects, and other non-tna inputs. "power_series" computes \(\mathrm{rowSums}(P + P^2 + \ldots + P^n)\) on the weighted matrix (with diag(P) := 0 when loops = FALSE) and matches tna::centralities(., measures = "Diffusion") byte-for-byte. For tna inputs, the default switches to "power_series" to match user expectation; pass diffusion_method = "kandhway_kuri" to force the binary-degree formula.

See also

centrality for computing multiple measures at once.

Examples

adj <- matrix(c(0, 1, 1, 1, 0, 1, 1, 1, 0), 3, 3)
rownames(adj) <- colnames(adj) <- c("A", "B", "C")
centrality_diffusion(adj)
#> A B C 
#> 6 6 6