Domain Proximity Prestige

Distance-weighted variant of domain prestige. For each directed node $v$: $$PD(v) = R_v^2 / (D_v \cdot (n - 1))$$ where $R_v$ is the number of other nodes that reach $v$, and $D_v$ is the sum of geodesic distances from those reachers to $v$. A node that is reachable quickly from many others scores high; unreachable nodes score 0.

Usage

centrality_prestige_domain_proximity(x, ...)

Arguments

x: Directed network input (matrix, igraph, cograph_network, tna object).
...: Additional arguments passed to centrality.

Value

Named numeric vector of domain proximity prestige values in $[0, 1]$.

Details

Bit-exact match against sna::prestige(cmode = "domain.proximity") on strongly connected directed graphs. Directed-only; returns NA with a warning on undirected input.

Divergence from sna on disconnected graphs

sna's formula computes (counts > 0) * gdist element-wise and then sums to get the denominator. For any pair where gdist = Inf (unreachable), R evaluates FALSE * Inf = NaN, so the entire denominator becomes NaN and sna zeros every node via p[is.nan(p)] <- 0. cograph masks with is.finite() before summing, producing mathematically correct values on any directed graph, including those with disconnected components.

References

Wasserman, S., & Faust, K. (1994). Social Network Analysis: Methods and Applications. Cambridge University Press.

Examples

# Directed 3-cycle: each node is reached by both others at distance 1 and 2
adj <- matrix(c(0,1,0, 0,0,1, 1,0,0), 3, 3, byrow = TRUE)
rownames(adj) <- colnames(adj) <- c("A", "B", "C")
centrality_prestige_domain_proximity(adj)
#>         A         B         C 
#> 0.6666667 0.6666667 0.6666667