Gould-Fernandez Brokerage — Coordinator Role

Coordinator brokerage (w_I): count of open directed 2-paths \(A \to V \to A\) passing through node \(V\), where all three nodes belong to \(V\)'s group. The broker mediates contact between two in-group members.

Usage

centrality_brokerage_coordinator(x, membership = NULL, ...)

Arguments

x

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

membership

Integer or character vector of group assignments, length equal to the number of nodes. Required.

...

Additional arguments passed to centrality.

Value

Named integer vector of coordinator role counts.

Details

Bit-exact match against sna::brokerage$raw.nli[, "w_I"]. Counts OPEN 2-paths only — those where no direct edge from a to c exists. Directed-only; returns NA with a warning on undirected input.

References

Gould, R. V., & Fernandez, R. M. (1989). Structures of mediation: A formal approach to brokerage in transaction networks. Sociological Methodology, 19, 89-126.

See also

centrality, centrality_brokerage_itinerant, centrality_brokerage_representative, centrality_brokerage_gatekeeper, centrality_brokerage_liaison.

Examples

adj <- matrix(c(0,1,1,0, 0,0,1,1, 0,0,0,1, 1,0,0,0), 4, 4, byrow = TRUE)
rownames(adj) <- colnames(adj) <- c("A", "B", "C", "D")
centrality_brokerage_coordinator(adj, membership = c(1, 1, 2, 2))
#> A B C D 
#> 0 0 0 0