Betweenness and closeness variants that carry a tuning parameter

Four measures that reweight, rescope or re-tune a measure centrality already computes. Each is a thin wrapper on centrality().

Usage

centrality_length_scaled_betweenness(x, ...)

centrality_delta_betweenness(x, betweenness_delta = 1, ...)

centrality_ego_betweenness(x, ...)

centrality_delta_closeness(x, mode = "all", closeness_delta = 1, ...)

Arguments

x: Network input: matrix, igraph, network, cograph_network, or tna object.
...: Additional arguments passed to centrality.
betweenness_delta: Decay exponent for centrality_delta_betweenness. Default 1.
mode: Direction: "all", "out" or "in".
closeness_delta: Distance exponent for centrality_delta_closeness. Default 1.

Value

Named numeric vector, one value per node.

Details

length_scaled_betweenness (Borgatti & Everett 2006; Brandes 2008, Algorithm 5): Betweenness with each separated pair weighted by \(1 / d(s,t)\), so brokering between nearby nodes counts for more than brokering across the graph.
delta_betweenness (Agneessens, Borgatti & Everett 2017): Betweenness with the pair weight \((d(s,t) - 1)^{-\delta}\) (betweenness_delta, default 1). At \(\delta = 0\) it is ordinary betweenness; raising it concentrates the score on locally brokered pairs.
ego_betweenness (Everett & Borgatti 2005): Betweenness computed inside the node's own ego network rather than the whole graph. A node with fewer than two neighbors scores 0. It is close to, but not a function of, effective_size.
delta_closeness (Agneessens, Borgatti & Everett 2017, eq. 2): \(\sum_j d_{ij}^{-\delta} / (n-1)\) (closeness_delta, default 1). One exponent spans the closeness family: \(\delta = 1\) is harmonic over \(n-1\), \(\delta = 2\) is harary over \(n-1\), a large \(\delta\) approaches degree, and \(\delta = 0\) counts the reachable set.

Bounded-distance betweenness, which the Centrality Zoo lists as "k-betweenness", needs no separate measure: it is centrality(x, measures = "betweenness", cutoff = k).

References

Agneessens, F., Borgatti, S. P., & Everett, M. G. (2017). Geodesic based centrality: Unifying the local and the global. Social Networks, 49, 12-26.

Brandes, U. (2008). On variants of shortest-path betweenness centrality and their generic computation. Social Networks, 30(2), 136-145.

Everett, M., & Borgatti, S. P. (2005). Ego network betweenness. Social Networks, 27(1), 31-38.

Examples

adj <- matrix(0, 6, 6)
adj[cbind(c(1, 1, 2, 4, 4, 5, 3), c(2, 3, 3, 5, 6, 6, 4))] <- 1
adj <- adj + t(adj)
rownames(adj) <- colnames(adj) <- LETTERS[1:6]
centrality_length_scaled_betweenness(adj)
#>        A        B        C        D        E        F 
#> 0.000000 0.000000 2.333333 2.333333 0.000000 0.000000 
centrality_delta_betweenness(adj, betweenness_delta = 2)
#> A B C D E F 
#> 0 0 3 3 0 0 
centrality_ego_betweenness(adj)
#> A B C D E F 
#> 0 0 2 2 0 0 
centrality_delta_closeness(adj, closeness_delta = 2)
#>         A         B         C         D         E         F 
#> 0.4944444 0.4944444 0.7000000 0.7000000 0.4944444 0.4944444