Gatekeeper Brokerage

Gatekeeper brokerage (Gould and Fernandez 1989) counts the open two-paths \(a \to v \to c\) through node \(v\) in which \(v\) and \(c\) belong to the same group and \(a\) to another group. The broker admits contact from outside to a member of its own group. A two-path is open when the network has no edge from \(a\) to \(c\). This role is \(b_{OI}\) in the notation of the source.

Usage

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

Arguments

x

Network input accepted by centrality.

membership

Group labels, one per node.

...

Further arguments to centrality, such as normalized.

Value

A named integer vector with one count per node, in input node order. normalized = TRUE returns a numeric vector.

Details

The measure is defined for directed networks. On an undirected network it returns NA with a cograph_undefined_measure warning, and the same happens when membership is missing, where the warning also has class cograph_bad_membership. A membership whose length differs from the number of nodes raises a cograph_bad_membership error. Group labels may be numbers or strings. Edge weights and self-loops are ignored.

References

Gould, R. V., & Fernandez, R. M. (1989). Structures of mediation: A formal approach to brokerage in transaction networks. Sociological Methodology, 19, 89-126. doi:10.2307/270949 .

See also

centrality_brokerage_representative, centrality_brokerage_coordinator, centrality.

Examples

centrality_brokerage_gatekeeper(regulation_net, membership = rep(1:2, each = 5))
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>          1          0          2          2          3          1          0 
#>   Evaluate     Create      Share 
#>          0          2          0